Question

Maria had $150 in gift certificates to use at a record store. She bought no more than 20 recordings. Each tape cost $5.95 and each CD cost 58.95. How many of each type of recording might she have bought?

Answer 1

Maria could have bought either 0 CDs and 20 tapes or 1 CD and 19 tapes.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's say Maria bought x tapes and y CDs. The cost of the tapes would be $5.95 * x, and the cost of the CDs would be $58.95 * y. We also know that the total cost of all the recordings cannot exceed $150. So we can write the equation:

5.95x + 58.95y <= 150

We also know that Maria bought no more than 20 recordings, so:

x + y <= 20

We can solve this system of equations to find the possible values of x and y.

Let's multiply the second equation by -5.95 and add it to the first equation to eliminate x:

-5.95x - 5.95y = -119

5.95x + 58.95y <= 150

After simplifying, we get:

53y <= 31

y <= 0.584

Since y represents the number of CDs, it must be a whole number. Therefore, Maria could have bought either 0 or 1 CD. If she bought 0 CDs, she could have bought a maximum of 20 tapes (x = 20). If she bought 1 CD, she could have bought a maximum of 19 tapes (x = 19).