Your friend gives you a gift card for $25.00. CDs cost $10.98 each plus 5.25% sales tax. You buy as many CDs as possible without having to pay extra money. What is the balance on the card after the purchase

The correct answer is $1.88.

Explanation:

Let x be the cost of a CD. Since each CD is $10.98, this gives us the expression

10.98x.

Tax is 5.25%. Percent means out of 100; this means we have 5.25/100=0.0525. We will multiply the cost of the CDs, 10.98x, by this:

0.0525 (10.98x)

We then add this to the cost of the CDs, to give us

10.98x+0.0525 (10.98x)

We do not want to spend any extra money; this means the total must be less than or equal to 25:

10.98x+0.0525 (10.98x) ≤25

Multiplying on the right, we have

10.98x+0.57645x ≤ 25

Combining like terms gives us

11.55645x ≤ 25

Divide both sides by 11.55645:

11.55645x/11.55645 ≤ 25/11.55645

x ≤ 2.11

Since we will not buy 0.11 of a CD, this gives us the solution

x ≤ 2.

We can buy at most 2 CDs.

Buying 2 CDs will cost 10.98*2 = 21.96.

The tax on this will be 0.0525*21.96 = 1.1529.

Together, this gives us 21.96+1.1529 = 23.1129 ≈ $23.12.

Out of the $25 gift card, we will have

25-23.12 = $1.88 left.