Question

Maya had $27. She spent all the money buying three burgers for x dollars each and two sandwiches for y dollars each. If Maya had bought two burgers and one sandwich, she would have been left with $11. The following system of equations models this scenario:

a. 3x+2y=27
b. 2x+y=16

Use the system of equations to solve for x and y.
a. (6,5)
b. (5,6)
c. (3,2)
d. (2,3)

Answer 1

By applying the elimination method to the system of equations, it was determined that the solution for the cost of one burger (x) and one sandwich (y) is (5, 6), which corresponds to option b.

Step-by-step explanation:

To solve for x and y using the given system of equations, we can apply the substitution or elimination method. We have two equations given:

1. 3x + 2y = 27
2. 2x + y = 16

Let's use the elimination method. We can multiply equation (2) by 2 to get a new equation (3):

4x + 2y = 32 (equation 3)

If we subtract equation (1) from equation (3), we get:

4x + 2y - (3x + 2y) = 32 - 27

x = 5

Now that we know the value of x, we can substitute it back into either equation (1) or (2) to solve for y. Let's use equation (2):

2(5) + y = 16

10 + y = 16

y = 6

Therefore, the solution to the system of equations is (x, y) = (5, 6), which corresponds to option b.