Question 79203
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.