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

Answer 1

Explanation:

The given system of equations models the scenario where Jason spent all of his money on buying CDs and magazines, and that if he had bought one more CD, he would have run out of money. The system of equations is:

4x + 2y = 32 (Equation 1)

5x + 2y = 36 (Equation 2)

The first equation represents the total amount of money Jason spent on 4 CDs (x dollars each) and 2 magazines (y dollars each). The second equation represents the total amount of money Jason would have spent if he had bought one more CD. By subtracting equation 1 from equation 2, we get:

x = 4 (Equation 3)

This equation tells us that each CD costs $4.

By substituting this value into equation 1, we get:

4(4) + 2y = 32

16 + 2y = 32

2y = 16

y = 8 (Equation 4)

This equation tells us that each magazine costs $8.

So, Jason spent $4 for each CD and $8 for each magazine.