Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Emma is a server at an all-you-can eat sushi restaurant. At one table, the customers ordered 3 child buffets and 2 adult buffets, which cost a total of $91. At another table, the customers ordered 3 child buffets and 4 adult buffets, paying a total of $131. How much does the buffet cost for each child and adult?

The cost for a child is $
, and the cost for an adult is $
.

Answer 1

Let \( c \) represent the cost of a child buffet, and \( a \) represent the cost of an adult buffet. We can set up a system of equations based on the information given:

1. From the first table with 3 child buffets and 2 adult buffets totaling $91:
\[
3c + 2a = 91
\]

2. From the second table with 3 child buffets and 4 adult buffets totaling $131:
\[
3c + 4a = 131
\]

Now we have the following system of equations:
\[
\begin{aligned}
1) & \quad 3c + 2a = 91 \\
2) & \quad 3c + 4a = 131
\end{aligned}
\]

Next, we can solve this system. We can eliminate \( c \) by subtracting equation 1 from equation 2:

\[
(3c + 4a) - (3c + 2a) = 131 - 91
\]

This simplifies to:
\[
2a = 40
\]

Now, divide both sides by 2 to solve for \( a \):
\[
a = 20
\]

Next, we substitute the value of \( a \) back into equation 1 to find \( c \):
\[
3c + 2(20) = 91
\]
\[
3c + 40 = 91
\]

Subtract 40 from both sides:
\[
3c = 51
\]

Now, divide by 3:
\[
c = 17
\]

Thus, the cost for a child buffet is \( $17 \) and the cost for an adult buffet is \( $20 \).

We can fill in the blanks:
The cost for a child is **$17**, and the cost for an adult is **$20**.