10
algebra

A meal delivery service has a base fee of $4.99 plus $0.75 per mile for delivery. To keep costs under $12, which inequality represents the maximum distance dd in miles?

A

0.75d+4.99<120.75d + 4.99 < 12

B

0.75d4.99<120.75d - 4.99 < 12

C

4.99d+0.75<124.99d + 0.75 < 12

D

0.75d+4.99>120.75d + 4.99 > 12

Correct Answer: A

Choice A is the correct answer. Total cost combines fixed and variable components.

  1. Fixed cost: $4.99 base fee
  2. Variable cost: $0.75 per mile for dd miles = 0.75d0.75d
  3. Total: 4.99+0.75d4.99 + 0.75d
  4. Constraint: "Under $12" means <12< 12: 0.75d+4.99<120.75d + 4.99 < 12

?�� Strategic Tip: "Under" means strictly less than (<<), while "at most" means less than or equal to (\leq).

Choice B is incorrect because it subtracts the base fee instead of adding it. Choice C is incorrect because it treats the base fee as the per-mile rate and vice versa. Choice D is incorrect because it uses >> instead of <<, representing costs exceeding $12 rather than staying under.