SOLUTION: My son and I can't find the solution to this question. 148 people attend a 5 day camp. The chef needs 9 lbs of food for each child and 12 lbs for each adult.He needs a total of 141

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Question 79203: My son and I can't find the solution to this question. 148 people attend a 5 day camp. The chef needs 9 lbs of food for each child and 12 lbs for each adult.He needs a total of 1410 lbs of food. How many children and how many adults attend camp? We figured that there are 26 adults and 122 children but we can't set it up using two variables. Please help!
Found 3 solutions by ankor@dixie-net.com, scott8148, Earlsdon:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website!
My son and I can't find the solution to this question. 148 people attend a 5 day camp. The chef needs 9 lbs of food for each child and 12 lbs for each adult.He needs a total of 1410 lbs of food. How many children and how many adults attend camp? We figured that there are 26 adults and 122 children but we can't set it up using two variables.:
:
Let a = number of adults; c = number children
:
Write and equation for each statement
" 148 people attend a 5 day camp."
a + c = 148
a = (148-c); to use for substitution
:
"The chef needs 9 lbs of food for each child and 12 lbs for each adult.He needs a total of 1410 lbs":
12a + 9c = 1410
:
"How many children and adults attend the camp"
Substitute (148-c) for a in the 2nd equation:
12(148-c) + 9c = 1410
1776 - 12c + 9c = 1410
-3c = 1410 - 1776
-3c = -366
c = -366/-3
c = +122
:
Easy enough to find a: 148-122 = 26

Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website!
always glad to help a parent

let a=number of adults and c=number of children ... a+c=148 ... a=148-c and (foodwise) 12a+9c=1410

substituting ... 12*(148-c)+9c=1410 ... 1776-3c=1410 ... c=122 ... and a=26

Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website!
Well...you have the correct answer!
Here's how you could set it up:
Let C = number of children and A = number of adults.
Now, there are 148 people attending the camp so:
1) C + A = 148 Rewrite this as: C = 148-C
Each child needs 9 lbs of food, so for C children, the chef needs (9 lbs)*(C).
Each adult needs 12 lbs of food, so for A adults, the chef needs (12 lbs)*(A).
The sum of these two quantities is 1410 lbs.
Now we can write the equations:
From 1) above:
2) C = 148-A and
3) 9C+12A = 1410 Substitute the C=148-A into this equation and solve for A
4) 9(148-A)+12A = 1410 Simplify.
1332-9A+12A = 1410 Combine like terms.
1332+3A = 1410 Subtract 1332 from both sides.
3A = 78 Divide both sides by 3.
A = 26 This is the number of adults in attendance.
C = 148-A
C = 148-26
C = 122 This is the number of children in attendance.