Question

Sonji went to a sandwich shop for lunch with 8 of her friends. Part of the group ordered only a sandwich for $5, and the rest of the group ordered a combo for $8. The bill for all 9 people totaled $66.00. Which system of equations represents the number of meals of each type that Sonji and her friends purchased?
x + y = 9. 5 x + 8 y = 66.
x + y = 66. 8 x + 5 y = 9.
x + y = 66. 5 x + 8 y = 9.
x + y = 9. 5 x minus 8 y = 66.

Answer 1

To represent the situation with a system of equations, we can define:

- \( x \): the number of sandwiches ordered (each costing $5)
- \( y \): the number of combos ordered (each costing $8)

From the problem, we know two things:

1. The total number of meals ordered by Sonji and her 8 friends is 9, which gives us the equation:
\[
x + y = 9
\]

2. The total cost of the meals is $66, which gives us the equation based on the prices:
\[
5x + 8y = 66
\]

Thus, the correct system of equations that represents the number of meals of each type that Sonji and her friends purchased is:
\[
\begin{align*}
x + y & = 9 \\
5x + 8y & = 66
\end{align*}
\]

So the correct choice is:
**\(x + y = 9\); \(5x + 8y = 66\)**.