Question

A restaurant catered a party for 40 people. A child’s dinner (c) cost $11 and an adult’s dinner (a) cost $20. The total cost of the dinner was $728. How many children and adults were at the party? Use the table to guess and check.

8 children and 32 adults
9 children and 31 adults
10 children and 30 adults
12 children and 28 adults

Answer 1

a+c=40

c=40-a

11c +20a=728

11(40-a)+20a=728

440-11a +20a=728

440+9a=728

9a = 288

a=288/9 = 32

32 adults

8 children

Answer 2

a + c = 40
20a + 11c = 728

Multiply equation # 1 by -11, then add the two equations together to clear the 'c' variable and solve for 'a'.

-11(a + c = 40)


20a + 11c = 728
-11a - 11c = -440
------------------------
9a  = 288
Divide both sides by 9
a = 32

a + c = 40
32 + c = 40
subtract 32 from both sides
c = 8

8 children and 32 adults; option 1