Set 9: Linear Functions (Advanced)

Explanation

Answer: A

A car rental costs $30/day. However, if you rent for more than 7 days, the cost is $25/day for every day after the 7th. Which equation models the cost $C$ for $d > 7$ days?

$C = 210 + 25(d - 7)$

✓ Correct

$C = 30d$

$C = 25d$

$C = 210 + 25d$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Piecewise logic. 1. First 7 days: $30\times 7 = 210$ . 2. Extra days: $d - 7$ . 3. Extra cost: $25(d - 7)$ . 4. Total: $210+ 25(d - 7)$ . Strategic Tip: Don't just multiply the new rate by total days ( $25d$ ). You must account for the first bracket separately. Choice B is incorrect because ignores discount. Choice C is incorrect because applies discount to all days. Choice D is incorrect because double counts days.

Key Steps:

•

The correct answer is $C = 210 + 25(d - 7)$

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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