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# In order to qualify for the year-end tennis tournament, Sam must win a

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Math Expert
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In order to qualify for the year-end tennis tournament, Sam must win a  [#permalink]

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21 Aug 2018, 05:57
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Difficulty:

25% (medium)

Question Stats:

78% (01:27) correct 22% (01:59) wrong based on 56 sessions

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In order to qualify for the year-end tennis tournament, Sam must win at least 60 percent of his matches this year. Presently Sam has won 14 of his 18 matches. Of Sams 13 matches remaining in the year, what is the least number that he must win in order to qualify for the year-end tournament?

A. 4
B. 5
C. 6
D. 7
E. 8

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In order to qualify for the year-end tennis tournament, Sam must win a  [#permalink]

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21 Aug 2018, 06:52
Total matches played by sam this year = 18 (already played) + 13(Remaining) = 31 Matches.
He has already won 14 of 18.
60% of 31 = 18.6 = almost equal to 19
So Sam must win 5 more matches.

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In order to qualify for the year-end tennis tournament, Sam must win a  [#permalink]

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21 Aug 2018, 07:16
Bunuel wrote:
In order to qualify for the year-end tennis tournament, Sam must win at least 60 percent of his matches this year. Presently Sam has won 14 of his 18 matches. Of Sams 13 matches remaining in the year, what is the least number that he must win in order to qualify for the year-end tournament?

A. 4
B. 5
C. 6
D. 7
E. 8

$$60$$% $$= \frac{3}{5}$$

Now, $$\frac{14 + x}{18 + 13} = \frac{3}{5}$$

Or, $$\frac{14 + x}{31} = \frac{3}{5}$$

Or, $$70 + 5x = 93$$

Or, $$x = \frac{23}{4}$$

So, $$x = 4.6$$ , Answer must be (B) 5
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In order to qualify for the year-end tennis tournament, Sam must win a   [#permalink] 21 Aug 2018, 07:16
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