jetblue777
Topic Author
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### Algebra: Solve This Problems

Got the idea from the math problem thread, this is a little bit complicated because it’s word problem. And No, this is not my homework. LOL. It was in the Integrated Algebra Regents (NY)

1) A group of 148 people is spending five days at summer camp. The cook ordered 12 pounds of food for each adult and 9 pounds for each child. A total of 1410 pounds of food was ordered. Find the total number of adults and children in the group.

You have to solve it by using elimination
Show All Work.

2) Find the perimeter of the square whose diagonal is 12. Write your answer in simplest radical form.

Enjoy
It's a cultural thing.

Ken777
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Joined: Thu Mar 11, 2004 5:39 am

### RE: Algebra: Solve This Problems

I'll pass on this one, however, as I'm on a diet.

dc9northwest
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### RE: Algebra: Solve This Problems

1) The total amount of adults and children in the group is 148--unless you count infants separately.

2) Too simple. I'm afraid I'll give it away if I say it.

Airstud
Posts: 3458
Joined: Wed Nov 29, 2000 11:57 am

### RE: Algebra: Solve This Problems

For the first one, all I've gotten so far is

c = number of childrens

12a + 9c = 1410

Except how bad am I at algebra? I have no clue what the next step is, that's how bad. Nice going.

The second one I think is pretty easy; the diagonal of a square cuts yon square into two right triangles; so we need only to use the Pythagorean theorem. The diagonal is the hypotenuse, and the hypotenuse squared equals the sum of the squares of the other two sides. So if the diagonal of the square is 12, its square of course is 144; and since this is a square we know the other two sides will be the same length; the sum of their squares must equal 144 so the square of each side is 72. The square root of 72 is 8.48528137etc; multiply this by cuatro and we get the perimameter: 33.9411254 etc.

Whew - I think I at least know something!

[Edited 2011-04-13 19:49:41]
Pancakes are delicious.

KingFriday013
Posts: 879
Joined: Fri May 18, 2007 7:56 am

### RE: Algebra: Solve This Problems

For #1:

Set up two equations:
12x 9y=1410 and x + y=148

Let's simplify the first one to 4x + 3y=470 (divide both sides by 3).
And the second one to 3x + 3y = 444 (multiply both sides by 3).

Note that both of these have the term "3y" in them.

So if we just subtract one from the other
(4x 3y) - (3x 3y) = 470 - 444 = 4x + 3y - 3x - 3y = 4x - 3x = x = 26

So we get x = 26.

At this point we can just plug in x to our original equation (either one).
x + y = 148 = 26 + y

Therefore:
148 - 26 = y = 122

So y = 122.

Therefore there were 26 adults and 122 children.

#2:

We know the diagonal is 12. Hence, by the Pythagorean Theorem, which states a2 + b2 = c2, and since the square has four identical sides (i.e., a = b):

122 = 144 = 2a2

We divide both sides by two and get
72 = a2

Take the square root of both sides and we get
√72 = √a2 = a

Since we have 4 sides, we multiply our value by 4, i.e., 4√72. This further simplifies to 24√2, which is the answer.

-J.

EDIT/NOTE: For some reason the plus signs aren't staying when I push "Post The Message!" If there's a blank space between the numbers then pretend there's a plus sign. If you want, send me a message through my profile and I'll just email this to you. j

[Edited 2011-04-13 19:58:33]
Tho' I've belted you an' flayed you, By the livin' Gawd that made you, You're a better man than I am, Gunga Din!

Maverick623
Posts: 4681
Joined: Thu Nov 30, 2006 9:13 am

### RE: Algebra: Solve This Problems

 Quoting Airstud (Reply 3):The square root of 72 is 8.48528137etc

Fail.

Still working on the first one...
"PHX is Phoenix, PDX is the other city" -777Way

Maverick623
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Joined: Thu Nov 30, 2006 9:13 am

### RE: Algebra: Solve This Problems

Gosh darn it.... it's always the simple steps that throw me off on these. I couldn't figure out how to merge the two equations.
"PHX is Phoenix, PDX is the other city" -777Way

trvyyz
Posts: 1331
Joined: Thu Oct 21, 2004 9:19 am

### RE: Algebra: Solve This Problems

2 unknowns need 2 equtions to solve
A+C=148 ie, C=148-A ------------ (1)
12A+9C=1410 ----------------------(2)
12A+9(148-A)=1410
=>3A=78; A=26, C=148-26=122

Second
12=sqrt(x^2+X^2)=Sqrt(2X^2)=Xsqrt(2)
=>X=12/sqrt(2)
perimeter=4X= 4*12/sqrt(2)=2*sqrt(2)*12=24*sqrt(2)
ie, 24√2

CXfirst
Posts: 2996
Joined: Tue Jan 30, 2007 8:13 pm

### RE: Algebra: Solve This Problems

1. Using Augmented Matrices (not that it is necessary for this easy example, but it is neater for presentation).

x = number of children

x + y = 148
9x + 12y = 1410

[ 1 1 | 148 ]
[ 9 12 | 1410 ]

[ 1 1 | 148 ]
[ 0 3 | 78 ] R2 --> R2 - 9xR1

using back substitution

3 y = 78
y = 26

x + y = 148
x + 26 = 148
x = 122

There are 122 children and 26 adults in the camp.

2.

The diagonal of a square is one which creates two right angle triangles, with a 2 angles of 45 degrees within them.

This is a special triangle with sides equivalent of a ratio 1:1:sqrt(2)

giving one side of the triangle length x, you get the ratio

x/1 = 12/sqrt(2)
x = sqrt(144)/sqrt(2)
x = sqrt 72

perimeter = 4x

p = 4sqrt(72)
p = 24sqrt(2) This is the simplest radical form

seb146
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Joined: Wed Dec 01, 1999 7:19 am

### RE: Algebra: Solve This Problems

The immediate area around JetBlue777 would be my answer...
 Quoting JetBlue777 (Thread starter):1) A group of 148 people is spending five days at summer camp. The cook ordered 12 pounds of food for each adult and 9 pounds for each child. A total of 1410 pounds of food was ordered. Find the total number of adults and children in the group.

148. People over-think things.
You say Merry Christmas, I say All Holidays Matter

DocLightning
Posts: 20562
Joined: Wed Nov 16, 2005 8:51 am

### RE: Algebra: Solve This Problems

I did this all 20 years ago. Since then I've earned three degrees.

I'm not doing it again.
-Doc Lightning-

"The sky calls to us. If we do not destroy ourselves, we will one day venture to the stars."
-Carl Sagan

Mir
Posts: 19374
Joined: Mon Jan 05, 2004 3:55 am

### RE: Algebra: Solve This Problems

 Quoting seb146 (Reply 9):Quoting JetBlue777 (Thread starter): 1) A group of 148 people is spending five days at summer camp. The cook ordered 12 pounds of food for each adult and 9 pounds for each child. A total of 1410 pounds of food was ordered. Find the total number of adults and children in the group. 148. People over-think things.

I like it.

And you're correct, too - if they had wanted the total numbers (plural) of adults and children, then you'd have to go through the whole simplifying two equations deal, but they already gave you the answer, so why bother?

Just goes to show that math people shouldn't try and write word problems without a grammatical consultant.

-Mir

[Edited 2011-04-13 22:58:14]
7 billion, one nation, imagination...it's a beautiful day

akiss20
Posts: 854
Joined: Tue Sep 04, 2007 9:50 am

### RE: Algebra: Solve This Problems

Let's step it up a notch

Comeon Doc, you got this!
Change will not come if we wait for some other person or some other time. We are the ones we've been waiting for. We are

DocLightning
Posts: 20562
Joined: Wed Nov 16, 2005 8:51 am

### RE: Algebra: Solve This Problems

 Quoting AKiss20 (Reply 12): Let's step it up a notch Comeon Doc, you got this!

As soon as you identify this diagnosis:

-Doc Lightning-

"The sky calls to us. If we do not destroy ourselves, we will one day venture to the stars."
-Carl Sagan

Mir
Posts: 19374
Joined: Mon Jan 05, 2004 3:55 am

### RE: Algebra: Solve This Problems

 Quoting DocLightning (Reply 13):As soon as you identify this diagnosis:

A kid is sick.

-Mir
7 billion, one nation, imagination...it's a beautiful day

DocLightning
Posts: 20562
Joined: Wed Nov 16, 2005 8:51 am

### RE: Algebra: Solve This Problems

 Quoting Mir (Reply 14): A kid is sick.

Yes. He's miserable. T=101.2° F (38.4° C) since Sunday, generally higher at night, lower in the morning. The ibuprofen makes it better for a few hours. He's not eating, either. And he itches. Oh, does that rash itch. Mom's tried Benadryl but it doesn't do anything.

You have to help him, Dr. Mir and Dr. Kiss! Look at the poor little guy!
-Doc Lightning-

"The sky calls to us. If we do not destroy ourselves, we will one day venture to the stars."
-Carl Sagan

Mir
Posts: 19374
Joined: Mon Jan 05, 2004 3:55 am

### RE: Algebra: Solve This Problems

 Quoting DocLightning (Reply 15):You have to help him, Dr. Mir and Dr. Kiss!

Hey, I'm not the one trying to one-up people with crazy technical knowledge. I have no clue what that is. My best WAG is some sort of food allergy - I had something like that once (though not nearly as extensive), and it went away in a few days. But I'm not a doctor, nor do I play one on TV, nor did I stay at a Holiday Inn Express last night, so...take that and \$6 and buy yourself a coffee at Starbucks.

In my experience, Benadryl doesn't do jack - the only thing it's good for is putting you to sleep. Which does make you stop itching, but only by virtue of being unconscious.

-Mir
7 billion, one nation, imagination...it's a beautiful day

KingFriday013
Posts: 879
Joined: Fri May 18, 2007 7:56 am

### RE: Algebra: Solve This Problems

I was really enjoying this thread... until all that happened...

Anyway, for the people who were saying #1 is simpler than it looks, I just assumed that the original poster meant to ask for the total number of adults and the total number of children as separate entities -- as would be expected on a NYS Regents Exam. They wouldn't do something stupid like that... and if they did, they would want the separate numbers as well.

-J.
Tho' I've belted you an' flayed you, By the livin' Gawd that made you, You're a better man than I am, Gunga Din!

Springbok747
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### RE: Algebra: Solve This Problems

אני תומך בישראל

Luftfahrer
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### RE: Algebra: Solve This Problems

Measles?
'He resembled a pilot, which to a seaman is trustworthiness personified.' Joseph Conrad

ojas
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### RE: Algebra: Solve This Problems

 Quoting JetBlue777 (Thread starter): 1) A group of 148 people is spending five days at summer camp. The cook ordered 12 pounds of food for each adult and 9 pounds for each child. A total of 1410 pounds of food was ordered. Find the total number of adults and children in the group. You have to solve it by using elimination Show All Work

Let number of adults be x, number of children be y.

So total people is x+y = 148 ---> equation (1)

9 lbs per child and 12 lbs per adult which comes to a total of 1410

12x + 9y = 1410 --> equation (2)

you have to solve these equations

12x + 9y = 1410 (2)
x + y = 148 (1)

Multiply (1) by 9

12x + 9y = 1410 (2)
9x + 9y = 1332 (1)

Now subtract .... do (2) - (1)

you get 3x = 78 (as 9y - 9y equals zero) which means x = 26 which means adults are 26 and the number of children are x + y = 148; 26 + y = 148; which means y = 122 which means there were 26 adults and 122 children

The area of a square is also expressed as "half of the product of the diagonals ". the rule is valid for all Rhombuses (i.e quadrilaterals with equal sides).

So the area of this Square = 1/2 * 12 * 12 = 72 sq. units

Which means length of each side is Square root of Area = sqrt of 72 = 6 * sqrt 2

So the premieter is 4 times the length of each side = 24 * sq rt of 2
Great leaders don't tell you what to do ... they show you how it's done!

DocLightning
Posts: 20562
Joined: Wed Nov 16, 2005 8:51 am

### RE: Algebra: Solve This Problems

 Quoting Mir (Reply 16): Hey, I'm not the one trying to one-up people with crazy technical knowledge. I have no clue what that is. My best WAG is some sort of food allergy - I had something like that once (though not nearly as extensive), and it went away in a few days.

I'll give you a big hint that if you google it, you will get the answer.

That tongue looks like a strawberry... (sorta). Strawberry Tongue.
-Doc Lightning-

"The sky calls to us. If we do not destroy ourselves, we will one day venture to the stars."
-Carl Sagan

seb146
Posts: 15368
Joined: Wed Dec 01, 1999 7:19 am

### RE: Algebra: Solve This Problems

 Quoting DocLightning (Reply 21):I'll give you a big hint that if you google it, you will get the answer.

Yes. I googled your hint and it became very obvious. I will give Mir a chance to respond.

 Quoting AKiss20 (Reply 12):Let's step it up a notch Comeon Doc, you got this!

My answer for this one is "banana"
You say Merry Christmas, I say All Holidays Matter

garnetpalmetto
Posts: 5351
Joined: Tue Oct 21, 2003 1:38 am

### RE: Algebra: Solve This Problems

Based on that back rash, I'd guess Scarlet Fever. No I'm not a doctor, though I often curse you people to the heavens. Why oh why can' t you people write medical records legibly?
South Carolina - too small to be its own country, too big to be a mental asylum.

baroque
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Joined: Thu Apr 27, 2006 2:15 pm

### RE: Algebra: Solve This Problems

 Quoting DocLightning (Reply 10):I did this all 20 years ago. Since then I've earned three degrees.

Reminds me of a old, old question from the 11+ exam in the UK. The following letters are part of an infinite series:

O..T..T..F..F..S..S

What are the next three letters in the series?

Plea for mercy, use only simple methods.

garnetpalmetto
Posts: 5351
Joined: Tue Oct 21, 2003 1:38 am

### RE: Algebra: Solve This Problems

 Quoting Baroque (Reply 24):Reminds me of a old, old question from the 11+ exam in the UK. The following letters are part of an infinite series: O..T..T..F..F..S..S What are the next three letters in the series? Plea for mercy, use only simple methods.

E..N..T

This one's rather simple. Each letter is the initial letter in a number (One, Two, Three, Four, Five, Six, Seven). Thus Eight, Nine, and Ten would be next.
South Carolina - too small to be its own country, too big to be a mental asylum.

Moose135
Posts: 2729
Joined: Mon Oct 04, 2004 11:27 pm

### RE: Algebra: Solve This Problems

 Quoting Baroque (Reply 24):O..T..T..F..F..S..S What are the next three letters in the series? Plea for mercy, use only simple methods.

E...N...T

Eight
Nine
Ten
KC-135 - Passing gas and taking names!

baroque
Posts: 12302
Joined: Thu Apr 27, 2006 2:15 pm

### RE: Algebra: Solve This Problems

Indeed. But it turns out that the success rate for 11 year olds is much much higher than for 20+. And even worse if you try it on unsuspecting mathematicians. The maths folk work out that the double letters are nearly symmetrical around the middle of the alphabet and the only thing that worries them is how a series starts out with single letters and then doubles.

All depends on how difficult a problem you think it is.

As someone remarked about the initial question
A group of 148 people is spending five days ...... Find the total number of adults and children in the group.

Dazed767
Posts: 4971
Joined: Tue May 18, 1999 11:55 am

### RE: Algebra: Solve This Problems

I suck at math, but that is scarlet fever.

dc9northwest
Posts: 2262
Joined: Sun Feb 04, 2007 5:33 am

### RE: Algebra: Solve This Problems

Geez, people actually solved the first problem   I'm surprised. I remember doing this sort of problem probably around 4th grade... But I'm in college-level Analysis now, and math does not include any numbers anymore

petertenthije
Posts: 3408
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### RE: Algebra: Solve This Problems

148 * 9 = 1332 - people multiplied by childrens portion to get minimum requirement of food
1410 - 1332 = 78 how much more food had been ordered above the minimum requirement
78 / (12-9) = 26 the amount of people that have bigger rations (= adults)
148 - 26 = 122 the kids

Thus: 122 kids and 26 adults calculated without the hassle of algebra.
Attamottamotta!

fridgmus
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### RE: Algebra: Solve This Problems

That's why I went to welding school, so I wouldn't have to do stuff like this!!!

F
The Lockheed Super Constellation, the REAL Queen of the Skies!

DocLightning
Posts: 20562
Joined: Wed Nov 16, 2005 8:51 am

### RE: Algebra: Solve This Problems

 Quoting garnetpalmetto (Reply 23): Based on that back rash, I'd guess Scarlet Fever.

DINGDINGDINGDING!!!

We have a winner!

And the most (academically) appropriate treatment is?

The treatment we'd actually use is?
-Doc Lightning-

"The sky calls to us. If we do not destroy ourselves, we will one day venture to the stars."
-Carl Sagan

akiss20
Posts: 854
Joined: Tue Sep 04, 2007 9:50 am

### RE: Algebra: Solve This Problems

 Quoting seb146 (Reply 22):Quoting AKiss20 (Reply 12): Let's step it up a notch Comeon Doc, you got this! My answer for this one is "banana"

That's my theory for questions I don't know, write something amusing and pray the graders have pity on me. I remember on one intro bio pset there was a question as to why some genetic disease was more prevalent in Eastern European cultures. I had no idea so I put some BS down about how EE cultures encouraged inbreeding in the elite. Answer was totally wrong but the grader wrote "hilarious! +5" and I called it a good day.

@Doc. Academically use penicillin, clindamycin or erythromycin? Actually, no idea
Change will not come if we wait for some other person or some other time. We are the ones we've been waiting for. We are

ANITIX87
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### RE: Algebra: Solve This Problems

Standard antibiotics. Pennicilin or erythromycin, IIRC. My dad had scarlet fever when he was little. And is a molecular biologist. So I've picked up some random knowledge I never thought I'd need.

TIS
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garnetpalmetto
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### RE: Algebra: Solve This Problems

 Quoting DocLightning (Reply 32): And the most (academically) appropriate treatment is? The treatment we'd actually use is?

Ship 'em off to a leper colony and be done with 'em?

Seriously not sure what the academically appropriate treatment is, but an antibiotic course, usually penicillin. If the kid is allergic, then erythromycin. Keep the tyke out of school so the little darling doesn't infect any other little darlings. No clue what to do with the rash or the itchiness though.
South Carolina - too small to be its own country, too big to be a mental asylum.

DocLightning
Posts: 20562
Joined: Wed Nov 16, 2005 8:51 am

### RE: Algebra: Solve This Problems

 Quoting ANITIX87 (Reply 34): Standard antibiotics. Pennicilin or erythromycin, IIRC.

Penicillin V-K is the most appropriate medication. Erythromycin (really, Azithromycin) is used in the truly allergic patient. In the patient who gets a "rash" for penicillin/amoxicillin, I use cephalexin, which has less than 10% cross-reactivity.

Group A Beta-hemolytic strep, which causes strep throat (and thus, scarlet fever) remains exquisitely sensitive to penicillin. That and syphilis are the only two bugs that have never evolved a way around good, old-fashioned Penicillin.

However, penicillin oral suspension tastes like fungus and must be dosed three times daily for ten days. So most of us use amoxicillin, which tastes like bubble gum and may be dosed twice daily.
-Doc Lightning-

"The sky calls to us. If we do not destroy ourselves, we will one day venture to the stars."
-Carl Sagan

Continental
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Joined: Sun Jun 25, 2000 3:46 am

### RE: Algebra: Solve This Problems

 Quoting DocLightning (Reply 36):Penicillin V-K is the most appropriate medication. Erythromycin (really, Azithromycin) is used in the truly allergic patient. In the patient who gets a "rash" for penicillin/amoxicillin, I use cephalexin, which has less than 10% cross-reactivity. Group A Beta-hemolytic strep, which causes strep throat (and thus, scarlet fever) remains exquisitely sensitive to penicillin. That and syphilis are the only two bugs that have never evolved a way around good, old-fashioned Penicillin. However, penicillin oral suspension tastes like fungus and must be dosed three times daily for ten days. So most of us use amoxicillin, which tastes like bubble gum and may be dosed twice daily.

Whew! Good thing he was treated or that could have led to rheumatic fever! Right? What a coincidence, I'm studying microbiology right now!

garnetpalmetto
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### RE: Algebra: Solve This Problems

I still like my suggestion of shipping them off to a leper colony
South Carolina - too small to be its own country, too big to be a mental asylum.

Maverick623
Posts: 4681
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### RE: Algebra: Solve This Problems

 Quoting DocLightning (Reply 36):However, penicillin oral suspension tastes like fungus

Well, penicillin being basically fungus dung....
 Quoting DocLightning (Reply 36):amoxicillin, which tastes like bubble gum

My best memories of being sick as a kid were getting prescribed amoxicillin. Yummm.
"PHX is Phoenix, PDX is the other city" -777Way

DocLightning
Posts: 20562
Joined: Wed Nov 16, 2005 8:51 am

### RE: Algebra: Solve This Problems

 Quoting Continental (Reply 37): Whew! Good thing he was treated or that could have led to rheumatic fever! Right? What a coincidence, I'm studying microbiology right now!

Acute Rheumatic Fever is a rare but very serious complication of Group A strep infections including scarlet fever. It tends to occur 1-3 weeks after the infection clears, assuming that the infection was not treated within 10 days of onset.

Acute Rheumatic Fever is an autoimmune phenomenon thought to be triggered by the "M" protein on the Streptococcus bacterium. In ARF, there is fever, rash, arthritis and, most importantly, inflammation of the valves of the heart. So this can cause long-term heart issues.

The vast majority of patients with untreated strep infections do not develop acute rheumatic fever, but the consequences are so dire that we are aggressive about diagnosing and treating these infections.

Scarlet fever is caused by a strain of Group A Strep that elaborates a toxin similar to that of poison ivy. So in addition to the sore throat, the child develops the characteristic rash. Scarlet fever was once a very serious illness, but in the last century the strains of bacteria that cause scarlatina seem to have gotten less virulent (which may or may not have anything to do with antibiotics) and so the kids are ill, but usually not frankly toxic. The treatment is the same as for any other strep infection, plus symptomatic treatment for the rash to make the child more comfortable while the antibiotics work their magic.
-Doc Lightning-

"The sky calls to us. If we do not destroy ourselves, we will one day venture to the stars."
-Carl Sagan

Mir
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### RE: Algebra: Solve This Problems

This thread is officially squawking 7500.

-Mir
7 billion, one nation, imagination...it's a beautiful day

jetblue777
Topic Author
Posts: 1204
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### RE: Algebra: Solve This Problems

 Quoting KingFriday013 (Reply 4): For #1: Set up two equations: 12x 9y=1410 and x + y=148 Let's simplify the first one to 4x + 3y=470 (divide both sides by 3). And the second one to 3x + 3y = 444 (multiply both sides by 3). Note that both of these have the term "3y" in them. So if we just subtract one from the other (4x 3y) - (3x 3y) = 470 - 444 = 4x + 3y - 3x - 3y = 4x - 3x = x = 26 So we get x = 26. At this point we can just plug in x to our original equation (either one). x + y = 148 = 26 + y Therefore: 148 - 26 = y = 122 So y = 122. Therefore there were 26 adults and 122 children. #2: We know the diagonal is 12. Hence, by the Pythagorean Theorem, which states a2 + b2 = c2, and since the square has four identical sides (i.e., a = b): 122 = 144 = 2a2 We divide both sides by two and get 72 = a2 Take the square root of both sides and we get √72 = √a2 = a Since we have 4 sides, we multiply our value by 4, i.e., 4√72. This further simplifies to 24√2, which is the answer. -J.

Yes, both answers are correct and with all the necessary steps that you have to write to get the full points on the NYS Regents.

 Quoting seb146 (Reply 9): Quoting JetBlue777 (Thread starter): 2) Find the perimeter of the square whose diagonal is 12. Write your answer in simplest radical form. The immediate area around JetBlue777 would be my answer...  Quoting JetBlue777 (Thread starter): 1) A group of 148 people is spending five days at summer camp. The cook ordered 12 pounds of food for each adult and 9 pounds for each child. A total of 1410 pounds of food was ordered. Find the total number of adults and children in the group. 148. People over-think things.

Now that you've mentioned it, they did mess up with the wording, but since it's a NYS Regents Exam, it's pure logic that you have to do all the algebraic steps and equations. Good catch, I shall tell my teacher tomorrow.
It's a cultural thing.

KingFriday013
Posts: 879
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### RE: Algebra: Solve This Problems

 Quoting JetBlue777 (Reply 42): Now that you've mentioned it, they did mess up with the wording, but since it's a NYS Regents Exam, it's pure logic that you have to do all the algebraic steps and equations. Good catch, I shall tell my teacher tomorrow.

They made mistakes like that when I took the Regents too. I don't think they'll ever learn...

-J.
Tho' I've belted you an' flayed you, By the livin' Gawd that made you, You're a better man than I am, Gunga Din!

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