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In order to qualify for the year-end tennis tournament, Sam must win at least 60 percent of his...

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In order to qualify for the year-end tennis tournament, Sam must win at least 60 percent of his...

by BTGmoderatorLU » Mon Jul 13, 2020 2:54 pm

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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 Sam`s 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

The OA is B
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Re: In order to qualify for the year-end tennis tournament, Sam must win at least 60 percent of his...

by swerve » Tue Jul 14, 2020 5:49 am
BTGmoderatorLU wrote: ↑
Mon Jul 13, 2020 2:54 pm
 Source: Magoosh

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 Sam`s 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

The OA is B
We have

\(60\% = \dfrac{3}{5}\)

Now,
\begin{align*}
\dfrac{14+x}{18+13} &= \dfrac{3}{5} \\
\dfrac{14+x}{31} &= \dfrac{3}{5} \\
70 + 5x &= 93 \\
x &= \dfrac{23}{4} = 4.6 \approx 5
\end{align*}

Therefore, B
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Re: In order to qualify for the year-end tennis tournament, Sam must win at least 60 percent of his...

by Scott@TargetTestPrep » Fri Jul 17, 2020 6:52 am
BTGmoderatorLU wrote: ↑
Mon Jul 13, 2020 2:54 pm
 Source: Magoosh

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 Sam`s 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

The OA is B
Solution:

We can let x be number of matches he must win in his remaining 13 matches and create the inequality:

(14 + x) / (18 + 13) ≥ 60/100

(14 + x) / 31 ≥ 3/5

5(14 + x) ≥ 3(31)

70 + 5x ≥ 93

5x ≥ 23

x ≥ 4.6

Since x must be an integer, the least possible value for x is 5.

Answer: B

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