2

Set 17: Systems of Equations (Advanced)

Explanation

Answer: C

An online store charges $15 per book plus $8 shipping. Another store charges $18 per book with free shipping. After how many books do both stores cost the same?

A.

1 book

B.

2 books

C.

3 books

✓ Correct
D.

4 books

Detailed Explanation

Choice C is correct. Choice C is the correct answer. Let bb be the number of books. Store 1: C1=15b+8C_1 = 15 b + 8 Store 2: C2=18bC_2 = 18 b Set equal: $$$15b + 8 = 18 b8= 3 b$b = \frac{8}{3} \approx 2.67 Since we need whole books, round up to 3. - 2 books: Store 1 = 38,Store2=36dollars(notequal)3books:Store1=38, Store 2 = 36 dollars (not equal) - 3 books: Store 1 = 53, Store 2 = 54 dollars (close) Strategic Tip: Break-even problems compare two linear cost models. Choice A is incorrect because costs are 24vs24 vs 18. Choice B is incorrect because costs are 39vs39 vs 36. Choice D is incorrect because costs are 69vs69 vs 72.

Key Steps:

The correct answer is 3 books

Why others are wrong:
A: Choice A is incorrect and may result from a calculation error.
B: Choice B is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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