Question

Jason had $32. He spent all the money buying four CDs for x dollars each and two magazines for y dollars each. If Jason had bought five CDs and two magazines, he would have run short by $4. The following system of equations models this scenario:

4x + 2y = 32
5x + 2y = 36

Use the system of equations to solve for x and y.

(4, 8)
(5, 6)
(8, 4)
(6, 5)

Answer 1

To solve this system of equations, we can use the method of substitution.

From the first equation, we can isolate x:
4x + 2y = 32
4x = 32 - 2y
x = 8 - 0.5y

Now we can substitute x in the second equation:
5(8 - 0.5y) + 2y = 36
40 - 2.5y + 2y = 36
-0.5y = -4
y = 8

Now that we have found y, we can substitute it back into the first equation to find x:
4x + 2(8) = 32
4x + 16 = 32
4x = 16
x = 4

Therefore, the solution to the system of equations is x = 4 and y = 8, which corresponds to the ordered pair (4, 8).

So the correct answer is: (4, 8)