JetBlue777 From United States of America, joined Jul 2009, 1554 posts, RR: 1 Posted (4 years 2 months 2 weeks 5 days 21 hours ago) and read 3497 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.

Ken777 From United States of America, joined Mar 2004, 8738 posts, RR: 9
Reply 1, posted (4 years 2 months 2 weeks 5 days 20 hours ago) and read 3480 times:

Airstud From United States of America, joined Nov 2000, 3000 posts, RR: 5
Reply 3, posted (4 years 2 months 2 weeks 5 days 20 hours ago) and read 3467 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.

KingFriday013 From United States of America, joined May 2007, 1304 posts, RR: 10
Reply 4, posted (4 years 2 months 2 weeks 5 days 20 hours ago) and read 3461 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 a^{2} + b^{2} = c^{2}, and since the square has four identical sides (i.e., a = b):

12^{2} = 144 = 2a^{2}

We divide both sides by two and get
72 = a^{2}

Take the square root of both sides and we get
√72 = √a^{2} = 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 From United States of America, joined Nov 2006, 5955 posts, RR: 7
Reply 5, posted (4 years 2 months 2 weeks 5 days 20 hours ago) and read 3454 times:

Maverick623 From United States of America, joined Nov 2006, 5955 posts, RR: 7
Reply 6, posted (4 years 2 months 2 weeks 5 days 20 hours ago) and read 3437 times:

seb146 From United States of America, joined Nov 1999, 12594 posts, RR: 14
Reply 9, posted (4 years 2 months 2 weeks 5 days 19 hours ago) and read 3377 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.

DocLightning From United States of America, joined Nov 2005, 21805 posts, RR: 63
Reply 10, posted (4 years 2 months 2 weeks 5 days 17 hours ago) and read 3343 times:

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

Mir From United States of America, joined Jan 2004, 22342 posts, RR: 55
Reply 11, posted (4 years 2 months 2 weeks 5 days 17 hours ago) and read 3333 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

AKiss20 From United States of America, joined Sep 2007, 699 posts, RR: 6
Reply 12, posted (4 years 2 months 2 weeks 5 days 17 hours ago) and read 3321 times:

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 From United States of America, joined Nov 2005, 21805 posts, RR: 63
Reply 13, posted (4 years 2 months 2 weeks 5 days 16 hours ago) and read 3299 times:

Mir From United States of America, joined Jan 2004, 22342 posts, RR: 55
Reply 14, posted (4 years 2 months 2 weeks 5 days 15 hours ago) and read 3296 times:

DocLightning From United States of America, joined Nov 2005, 21805 posts, RR: 63
Reply 15, posted (4 years 2 months 2 weeks 5 days 15 hours ago) and read 3292 times:

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!

Mir From United States of America, joined Jan 2004, 22342 posts, RR: 55
Reply 16, posted (4 years 2 months 2 weeks 5 days 15 hours ago) and read 3288 times:

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

KingFriday013 From United States of America, joined May 2007, 1304 posts, RR: 10
Reply 17, posted (4 years 2 months 2 weeks 5 days 13 hours ago) and read 3260 times:

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!

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

DocLightning From United States of America, joined Nov 2005, 21805 posts, RR: 63
Reply 21, posted (4 years 2 months 2 weeks 5 days 8 hours ago) and read 3158 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.

seb146 From United States of America, joined Nov 1999, 12594 posts, RR: 14
Reply 22, posted (4 years 2 months 2 weeks 5 days 7 hours ago) and read 3126 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.

garnetpalmetto From United States of America, joined Oct 2003, 5483 posts, RR: 52
Reply 23, posted (4 years 2 months 2 weeks 5 days 7 hours ago) and read 3114 times:

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 From Australia, joined Apr 2006, 15380 posts, RR: 59
Reply 24, posted (4 years 2 months 2 weeks 5 days 7 hours ago) and read 3110 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

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 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 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 garnetpalmetto
: I still like my suggestion of shipping them off to a leper colony

39 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 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.