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13 Feb 2020, 07:46
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C
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Difficulty:
55%
(hard)
Question Stats:
68% (02:53) correct
32%
(03:07)
wrong
based on 217
sessions
History
Date
Time
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Not Attempted Yet
Amy's sells kale at x dollar per pound for the first 20 pounds and 0.8x for every subsequent pound. Lucia's price is x per pound for the first 14 pounds and 0.9x for subsequent pounds. What is the minimum number of pounds over 15 for which Amy's becomes an equal or better deal?
A. 24
B. 25
C. 26
D. 27
E. 28
Are You Up For the Challenge: 700 Level Questions
A. 24
B. 25
C. 26
D. 27
E. 28
Are You Up For the Challenge: 700 Level Questions
21 Feb 2020, 09:04
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Bunuel
We can create the inequality:
20x + 0.8x(T - 20) ≤ 14x + 0.9x(T - 14)
20 + 0.8(T - 20) ≤ 14 + 0.9(T - 14)
6 + 0.8T - 16 ≤ 0.9T - 12.6
2.6 ≤ 0.1T
26 ≤ T
Answer: C
General Discussion
13 Feb 2020, 08:01
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For the six pounds between the 14th and 20th pound, you save 0.1x dollars by buying from Lucia. But after the 20th pound, you save 0.1x dollars by buying from Amy. So for the prices to be equal buying from either person, you'd need to buy six pounds beyond the first 20, and the answer is 26 pounds.
The wording of the question is confusing though -- when it asks for "the minimum number of pounds over 15", I think you could legitimately interpret the question to be asking how many pounds we would need to add to a 15 pound purchase to arrive at equal prices (in which case the answer would be 11). That's not the intended meaning though.
The wording of the question is confusing though -- when it asks for "the minimum number of pounds over 15", I think you could legitimately interpret the question to be asking how many pounds we would need to add to a 15 pound purchase to arrive at equal prices (in which case the answer would be 11). That's not the intended meaning though.
