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

Question

Mathematics

Liam Adams

13 December, 04:36

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

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Answers (1)

Know the Answer?

Delgado · Answer 1

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.