Chapter 11.5, Problem 10P

Solve each equation. Check your solution.

$\frac{2}{p+3}=\frac{7}{28p}$

To determine

To solve the equation and check the solutions.

Answer to Problem 10P

The solution is $p=\frac{3}{7}$ .

Explanation of Solution

Given information:

The given equation is:

  $\frac{2}{p+3}=\frac{7}{28p}$

Calculation:

The solution can be obtained by:

  $\begin{array}{l}\frac{2}{p+3}=\frac{7}{28p}\\ 2\left(28p\right)=7\left(p+3\right)\\ 56p=7p+21\\ 56p-7p=21\\ 49p=21\\ p=\frac{21}{49}\\ p=\frac{3}{7}\end{array}$

Hence, the solution is $p=\frac{3}{7}$ .

The solution can be checked by:

  $\begin{array}{l}\frac{2}{p+3}=\frac{7}{28p}\\ \frac{2}{\frac{3}{7}+3}=\frac{7}{28\left(\frac{3}{7}\right)}\\ \frac{2\times 7}{24}=\frac{7}{12}\\ \frac{14}{24}=\frac{7}{12}\\ \frac{7}{12}=\frac{7}{12}\end{array}$

The solution is correct.