# You have 72 hits in 160 times at bat. Your batting average is or 0.45. How many consecutive hits must 160 you get to increase your batting average to 0.56?

Jun 30, 2017

See a solution process below:

#### Explanation:

We can write the equation to solve this problem as:

$\frac{72 + h}{160 + h} = 0.560$

Where $h$ is the number of consecutive hits need.

Solving for $h$ gives:

$\textcolor{red}{\left(160 + h\right)} \times \frac{72 + h}{160 + h} = \textcolor{red}{\left(160 + h\right)} \times 0.560$

$\cancel{\textcolor{red}{\left(160 + h\right)}} \times \frac{72 + h}{\textcolor{red}{\cancel{\textcolor{b l a c k}{160 + h}}}} = \left(\textcolor{red}{160} \times 0.560\right) + \left(\textcolor{red}{h} \times 0.560\right)$

$72 + h = 89.6 + 0.560 h$

$- \textcolor{red}{72} + 72 + h - \textcolor{b l u e}{0.560 h} = - \textcolor{red}{72} + 89.6 + 0.560 h - \textcolor{b l u e}{0.560 h}$

$0 + \left(1 - \textcolor{b l u e}{0.560}\right) h = 17.6 + 0$

$0.44 h = 17.6$

$\frac{0.44 h}{\textcolor{red}{0.44}} = \frac{17.6}{\textcolor{red}{0.44}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{0.44}}} h}{\cancel{\textcolor{red}{0.44}}} = 40$

$h = 40$

You will need $\textcolor{red}{40}$ consecutive hits to move your batting average from 0.450 to 0.560