Bunuel wrote:

A roller coaster park offers two types of passes. Pass A costs $100 and entitles its holder up to 10 rides at no extra cost, and every ride in excess of 10 at a cost of $5 per ride. Pass B costs $10 and entitles its holder to one ride at no cost and each extra ride for $9. What is the least number of rides taken that would make Pass A a better deal than Pass B?

A. 13

B. 12

C. 11

D. 10

E. 9

Answer choices can be used if setting up the inequality is difficult.

Pass A: $100 for 10 rides; $5 each after 10 rides

Pass B: $10 for 1 ride; $9 each after 1 ride

Start with C to get a benchmark.

Answer C) 11 ridesPass A: 10 rides =

$100. +1 ride =

$5 Pass A Total:

$105Pass B: 1 ride=

$10. Plus 10 rides * $9 =

$90 Pass B total:

$10011 rides is too few. Even at $9 per extra ride, for 11 rides, Pass B

equals the cost of Pass A.

We need more rides so that the $9 per ride vs. $5 per ride will have an effect (will make B more costly than A). Eliminate answers D and E

Answer B) 12 ridesUse Answer C cost for each (11 rides) + cost of one more ride (=12 rides)

For A, cost of 11=$105, + $5*(1 more ride): $110

For B, cost of 11=$100, + $9*(1 more ride): $109

Pass B is still a better deal than Pass A. By POE, the answer is A. Check:

Answer A) 13 ridesFor A, add $5 to cost in answer B (+1 ride): $115

For B, add $9 to cost in answer B: $118

Pass B cost > Pass A cost at 13 rides

ANSWER A
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At the still point, there the dance is. -- T.S. Eliot

Formerly genxer123