# 1/3 of a number is added to 5. The result is one and a half times the original number. Find the...

## Question:

{eq}\frac {1}{3} {/eq} of a number is added to {eq}5 {/eq}. The result is one and a half times the original number.

Find the number.

## Simple Algebra:

Many problems we deal with in mathematics require the conversion of English sentences into mathematical expressions. These kinds of problems come under simple algebra.

Given:

• {eq}\displaystyle \frac{1}{3} {/eq} of a number is added to 5.
• The result is one and a half times the original number.

Let's assume the number to be x.

The mathematical representation of the given sentences:

{eq}\displaystyle \begin{align} \frac{1}{3} \times x + 5 &= \frac{1}{2} \times x \\ \frac{x}{3} + 5 &= \frac{x}{2} \\ \frac{x}{3} - \frac{x}{2} &= -5 \\ \frac{2x - 3x}{6} &= -5 \\ -\frac{x}{6} &= -5 \\ x &= 5 (6) \\ &= 30 \end{align} {/eq}

Therefore, the required number is 30.