Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. Carly is a server at an all-you-can eat sushi restaurant. At one table, the customers ordered 4 child buffets and 2 adult buffets, which cost a total of $120. At another table, the customers ordered 3 child buffets and 3 adult buffets, paying a total of $132. How much does the buffet cost for each child and adult? The cost for a child is $ and the cost for an adult is $ Submit

Answer 1

1) Gathering the data

4 child buffets + 2 adult buffets = $120

3 child buffets + 3 adult buffets = $132

Let's call child buffet 'c' and adult buffet by 'a' and then set the system

4c +2a = 120

3c +3a=132

2) Solving the system by elimination method

4c +2a = 120 Multiply by -3 t

3c +3a=132 Multiply by 2

-12c -6a = -360 Adding both equations, we can eliminate one variable

6c -6a = 264

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-6c =-96

6c = 96 Divide both sides by 6

c=16

2.2 Let's plug that into one of those original equations, usually the simplest one

3c +3a = 132

3(16) +3a = 132

48 + 3a = 132 Subtract 48 from both sides

3a =132-48

3a=84 Divide both sides by 3

a=28

3) So the answers are:

How much does the buffet cost for each child and adult?

Each child: $16 Each adult: $28