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For two full weeks, Karen studied every day for her big test. On weekd

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For two full weeks, Karen studied every day for her big test. On weekd  [#permalink]

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New post 22 Sep 2018, 23:07
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For two full weeks, Karen studied every day for her big test. On weekdays, she studied an average of x hours per day, and on the weekend, she studied an average of y hours per day. Her average for the whole two weeks was 50% greater than her average during the weekdays. What is the value of \(\frac{x}{y}\)?


A) \(\frac{2}{11}\)

B) \(\frac{4}{21}\)

C) \(\frac{4}{11}\)

D) 4

E) 8

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Re: For two full weeks, Karen studied every day for her big test. On weekd  [#permalink]

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New post 23 Sep 2018, 00:52
(10*x + 4*y)/14 = 1.5(10*x/10)

Solving above equation, we get x/y = 4/11

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Re: For two full weeks, Karen studied every day for her big test. On weekd  [#permalink]

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New post 23 Sep 2018, 00:59

Solution



Given:
    • For two full weeks, Karen studied every day for her big test
    • On weekdays, she studied an average of x hours per day
    • On the weekend, she studied an average of y hours per day
    • Her average for the whole two weeks was 50% greater than her average during the weekdays

To find:
    • The value of \(\frac{x}{y}\)

Approach and Working:
Total study time in the weekdays = 10 * x = 10x hours
Total study time in the weekends = 4 * y = 4y hours
Hence, total study time in two weeks = (10x + 4y) hours

As per the question,
    • \(\frac{10x + 4y}{14} = x * \frac{3}{2}\)
    Or, 20x + 8y = 42x
    Or, 22x = 8y
    Or, \(\frac{x}{y} = \frac{8}{22} = \frac{4}{11}\)

Hence, the correct answer is option C.

Answer: C
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Re: For two full weeks, Karen studied every day for her big test. On weekd &nbs [#permalink] 23 Sep 2018, 00:59
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