Question

Jason had $32. He spent all the money on buying 4 CDs for $x each and 2 magazines for $y each. If Jason had bought 5 CDs and 2 magazines, he would have run short of $4.
A student concluded that the price of each CD is $5 and the price of each magazine is $6. Which statement best justifies whether the student's conclusion is correct or incorrect?
The student's conclusion is incorrect because the solution to the system of equations 4x + 2y = 4 and 5x + 2y = 36 is (9, 4).
The student's conclusion is incorrect because the solution to the system of equations 4x + 2y = 32 and 5x + 2y = 36 is (4, 8).
The student's conclusion is correct because the solution to the system of equations 4x + 2y = 4 and 5x + 2y = 36 is (5, 6).
The student's conclusion is correct because the solution to the system of equations 4x + 2y = 32 and 5x + 2y = 36 is (5, 6).

Answer 1

You can set up two equations from the information given. I will set them up for you:

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

Let's solve the first equation to come up with a value for y.

32 = 4x + 2y
32 - 4x = 2y
16 - 2x = y

Now we plug y into the other equation.

36 = 5x + 2(16-2x)
36 = 5x + 32 - 4x
4 = x

Now we have our real x value and we can plug it into the first equation.

32 = 4(4) + 2y
32 = 16 + 2y
16 = 2y
8 = y

Since x = 4 and y = 8, you get the final coordinates of (4,8).

Your answer is the second statement provided above.