Question

The ratio of a to b is$\frac{2}{3}$. The sum of a and b is $10$. What is the ratio of $a+b$ to $b-a$?

Short answer

The ratio is $5$.

Step-by-step solution

Step 1. Given information.

Consider the given question,

$$\begin{gathered} \frac{a}{b}=\frac{2}{3}......\left(i\right) \\ a+b=10......\left(ii\right) \end{gathered}$$

Solve equation (ii) for a,

$a=10-b$

Substitute the value of a in equation (i),

$$\begin{gathered} \frac{10-b}{b}=\frac{2}{3} \\ 30-3b=2b \\ b=6 \end{gathered}$$

Step 2. Find the value of a.

Substitute the value of bin equation (ii),

$$\begin{gathered} a+6=10 \\ a=4 \end{gathered}$$

Then,

$$\begin{gathered} b-a=6-4 \\ b-a=2 \end{gathered}$$

Therefore, the required ration is given below,

$$\begin{gathered} \frac{a+b}{b-a}=\frac{10}{2} \\ \frac{a+b}{b-a}=5 \end{gathered}$$