Question

The tennis team has played $28$ matches so far this season.

They have won $10$ matches so far.

How many matches will the team need to win for the team to have a $55\%$ success rate?

• A. $3$
• B. $8$
• C. $12$
• D. $18$

Answer 1

The correct option is C

$12$

Explanation for the correct option:

The success rate is defines as $\frac{numberofsuccess}{numberoftrials}$.

Suppose the number of match to be win is $x$.

Therefore the the total matches will be $28+x$.

and the total number of won match will be $10+x$.

Now equate $55\%$ with the given formula to obtain the value of $x$.

$\frac{55}{100}=\frac{10+x}{28+x}$

Cross multiply in the obtained expression to simplify..

$$\begin{gathered} 55(28+x)=100(10+x) \\ \Rightarrow 1540+55x=1000+100x\left[\mathrm{Eliminating}\mathrm{the}\mathrm{parentheses}\right] \\ \Rightarrow 1540-1000=100x-55x[\mathrm{Grouping}\mathrm{constant}\mathrm{and}x\mathrm{term}\mathrm{in}\mathrm{each}\mathrm{side}] \\ \Rightarrow 540=45x \\ \Rightarrow x=\frac{540}{45}\left[\mathrm{Dividing}45\mathrm{on}\mathrm{both}\mathrm{sides}\right] \\ \therefore x=12 \end{gathered}$$

Hence, option $\left(C\right)$ is correct.