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Algebra: Solve This Problems  
User currently offlineJetBlue777 From Canada, joined Jul 2009, 1451 posts, RR: 1
Posted (3 years 3 months 2 weeks 4 days 13 hours ago) and read 2829 times:

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.
43 replies: All unread, showing first 25:
 
User currently offlineKen777 From United States of America, joined Mar 2004, 8190 posts, RR: 8
Reply 1, posted (3 years 3 months 2 weeks 4 days 12 hours ago) and read 2812 times:

I liked the other math thread - the answer was 2.

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


User currently offlinedc9northwest From Switzerland, joined Feb 2007, 2269 posts, RR: 7
Reply 2, posted (3 years 3 months 2 weeks 4 days 12 hours ago) and read 2804 times:

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.


User currently offlineAirstud From United States of America, joined Nov 2000, 2638 posts, RR: 3
Reply 3, posted (3 years 3 months 2 weeks 4 days 12 hours ago) and read 2799 times:

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

a = number of adults
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.
User currently offlineKingFriday013 From United States of America, joined May 2007, 1296 posts, RR: 9
Reply 4, posted (3 years 3 months 2 weeks 4 days 12 hours ago) and read 2793 times:

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!
User currently offlineMaverick623 From United States of America, joined Nov 2006, 5569 posts, RR: 6
Reply 5, posted (3 years 3 months 2 weeks 4 days 12 hours ago) and read 2786 times:

Quoting JetBlue777 (Thread starter):

Write your answer in simplest radical form.
Quoting Airstud (Reply 3):
The square root of 72 is 8.48528137etc

Fail.

Answer is 24√2

Still working on the first one...



"PHX is Phoenix, PDX is the other city" -777Way
User currently offlineMaverick623 From United States of America, joined Nov 2006, 5569 posts, RR: 6
Reply 6, posted (3 years 3 months 2 weeks 4 days 12 hours ago) and read 2769 times:

Quoting KingFriday013 (Reply 4):
Let's simplify

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
User currently offlinetrvyyz From Canada, joined Oct 2004, 1369 posts, RR: 10
Reply 7, posted (3 years 3 months 2 weeks 4 days 12 hours ago) and read 2751 times:

Quoting KingFriday013 (Reply 4):

  
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


User currently offlineCXfirst From Norway, joined Jan 2007, 3037 posts, RR: 1
Reply 8, posted (3 years 3 months 2 weeks 4 days 11 hours ago) and read 2724 times:

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

x = number of children
y = number of adults

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



From Norway, live in Australia
User currently offlineseb146 From United States of America, joined Nov 1999, 11533 posts, RR: 15
Reply 9, posted (3 years 3 months 2 weeks 4 days 11 hours ago) and read 2709 times:

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.



Life in the wall is a drag.
User currently offlineDocLightning From United States of America, joined Nov 2005, 19415 posts, RR: 58
Reply 10, posted (3 years 3 months 2 weeks 4 days 9 hours ago) and read 2675 times:

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

I'm not doing it again.


User currently offlineMir From United States of America, joined Jan 2004, 21528 posts, RR: 55
Reply 11, posted (3 years 3 months 2 weeks 4 days 9 hours ago) and read 2665 times:

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
User currently offlineAKiss20 From United States of America, joined Sep 2007, 603 posts, RR: 5
Reply 12, posted (3 years 3 months 2 weeks 4 days 9 hours ago) and read 2653 times:

http://i.imgur.com/nzdmf.jpg

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
User currently offlineDocLightning From United States of America, joined Nov 2005, 19415 posts, RR: 58
Reply 13, posted (3 years 3 months 2 weeks 4 days 8 hours ago) and read 2631 times:

Quoting AKiss20 (Reply 12):

Let's step it up a notch

Comeon Doc, you got this!

As soon as you identify this diagnosis:

http://aapredbook.aappublications.org/content/images/large/2006/1/124_79.jpeg


User currently offlineMir From United States of America, joined Jan 2004, 21528 posts, RR: 55
Reply 14, posted (3 years 3 months 2 weeks 4 days 7 hours ago) and read 2628 times:

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
User currently offlineDocLightning From United States of America, joined Nov 2005, 19415 posts, RR: 58
Reply 15, posted (3 years 3 months 2 weeks 4 days 7 hours ago) and read 2624 times:

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!


User currently offlineMir From United States of America, joined Jan 2004, 21528 posts, RR: 55
Reply 16, posted (3 years 3 months 2 weeks 4 days 7 hours ago) and read 2620 times:

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.

Quoting DocLightning (Reply 15):
Mom's tried Benadryl but it doesn't do anything.

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
User currently offlineKingFriday013 From United States of America, joined May 2007, 1296 posts, RR: 9
Reply 17, posted (3 years 3 months 2 weeks 4 days 5 hours ago) and read 2592 times:

Quoting AKiss20 (Reply 12):
Quoting DocLightning (Reply 13):
Quoting Mir (Reply 14):
Quoting DocLightning (Reply 15):
Quoting Mir (Reply 16):

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!
User currently offlineSpringbok747 From Australia, joined Nov 2004, 4387 posts, RR: 10
Reply 18, posted (3 years 3 months 2 weeks 4 days 5 hours ago) and read 2580 times:

Quoting DocLightning (Reply 13):

Addisons disease?



אני תומך בישראל
User currently offlineLuftfahrer From Germany, joined Mar 2009, 1012 posts, RR: 2
Reply 19, posted (3 years 3 months 2 weeks 4 days 3 hours ago) and read 2542 times:

Quoting DocLightning (Reply 13):

Measles?



Et là tu montes encore plus haut et ça persiste, alors on vole
User currently offlineojas From India, joined Mar 2008, 2963 posts, RR: 24
Reply 20, posted (3 years 3 months 2 weeks 4 days 3 hours ago) and read 2525 times:

Quoting KingFriday013 (Reply 4):
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

Quoting JetBlue777 (Thread starter):
2) Find the perimeter of the square whose diagonal is 12. Write your answer in simplest radical form.

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



A lion does not concern himself with the opinions of the sheep
User currently offlineDocLightning From United States of America, joined Nov 2005, 19415 posts, RR: 58
Reply 21, posted (3 years 3 months 2 weeks 4 days ago) and read 2490 times:

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.


User currently offlineseb146 From United States of America, joined Nov 1999, 11533 posts, RR: 15
Reply 22, posted (3 years 3 months 2 weeks 3 days 23 hours ago) and read 2458 times:

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"



Life in the wall is a drag.
User currently offlinegarnetpalmetto From United States of America, joined Oct 2003, 5364 posts, RR: 53
Reply 23, posted (3 years 3 months 2 weeks 3 days 23 hours ago) and read 2446 times:

Quoting DocLightning (Reply 13):

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.
User currently offlineBaroque From Australia, joined Apr 2006, 15380 posts, RR: 59
Reply 24, posted (3 years 3 months 2 weeks 3 days 23 hours ago) and read 2442 times:

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.


25 garnetpalmetto : 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
26 moose135 : E...N...T Eight Nine Ten
27 Baroque : 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 mathem
28 Dazed767 : I suck at math, but that is scarlet fever.
29 Post contains images dc9northwest : 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-le
30 petertenthije : 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
31 fridgmus : That's why I went to welding school, so I wouldn't have to do stuff like this!!! F
32 DocLightning : DINGDINGDINGDING!!! We have a winner! And the most (academically) appropriate treatment is? The treatment we'd actually use is?
33 AKiss20 : 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
34 ANITIX87 : 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
35 Post contains images garnetpalmetto : 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, usu
36 DocLightning : Penicillin V-K is the most appropriate medication. Erythromycin (really, Azithromycin) is used in the truly allergic patient. In the patient who gets
37 Continental : Whew! Good thing he was treated or that could have led to rheumatic fever! Right? What a coincidence, I'm studying microbiology right now!
38 Post contains images garnetpalmetto : I still like my suggestion of shipping them off to a leper colony
39 Post contains images Maverick623 : Well, penicillin being basically fungus dung.... My best memories of being sick as a kid were getting prescribed amoxicillin. Yummm.
40 DocLightning : 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
41 Mir : This thread is officially squawking 7500. -Mir
42 Post contains images JetBlue777 : 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. Now that you've ment
43 KingFriday013 : They made mistakes like that when I took the Regents too. I don't think they'll ever learn... -J.
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