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?

Question

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: $$\begin{array}{rlr}x+y& =95x+8y& =66\end{array}$$

So the correct choice is: $x+y=9$; $5x+8y=66$.