10

Set 15: Linear Inequalities

Explanation

Answer: A

A cloud storage service charges $12per month for 100 GB. Each additional 50 GB costs \5. If someone has a monthly budget of at most $32, which inequality represents the maximum number of additional 50 GB blocks $$b$ they can purchase?

A.

5b+12325b + 12 \leq 32

✓ Correct
B.

12b+53212b + 5 \leq 32

C.

5b12325b - 12 \leq 32

D.

17b3217b \leq 32

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Base fee plus variable costs create a linear inequality. 1. Base cost: $12for basic 100 GB 2. Variable cost: \5 per additional 50 GB block 3. Total: 12 + 5 b$$ for b blocks 4. Budget: At most \$$32means $$\leq 32 5. Result: 5b+12325b + 12 \leq 32 Strategic Tip: Identify fixed costs vs variable costs when modeling real-world scenarios. Choice B is incorrect because it reverses the coefficients (base fee and per-unit cost). Choice C is incorrect because it subtracts the base fee instead of adding it. Choice D is incorrect because it adds the coefficients together, losing the structure of fixed + variable costs.

Key Steps:

The correct answer is 5b+12325b + 12 \leq 32

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