Chapter 7.5, Problem 12E

To determine

To find: The number of consecutive hits.

Answer to Problem 12E

The number of consecutive hits are $15$ .

Explanation of Solution

Given:

The given equation is:

  $0.360=\frac{12+x}{60+x}$

Here $x$ are the number of consecutive hits.

The solution is calculated as:

  $\begin{array}{c}0.360=\frac{12+x}{60+x}\\ 0.360\left(60+x\right)=\left(12+x\right)\left[\text{cross multiply}\right]\\ 21.6+0.360x=12+x\\ 0.640x=9.6\end{array}$

Further simplified as:

  $x=\frac{9.6}{\begin{array}{l}0.640\\ x=15\end{array}}$

Check for $x=15$ is the solution of the equation.

  $\begin{array}{c}0.360=\frac{12+x}{60+x}\\ \frac{36}{100}=\frac{12+15}{60+15}\\ \frac{9}{25}=\frac{9}{25}\left[\text{true}\right]\end{array}$

Hence, the number of consecutive hits are $15$ .