Two-thirds of a number is 5 more than half of it. What is the number?

Given:

Two-thirds of a number is 5 more than half of it.

To do:

We have to find the number.

Solution:

Let the number be $x$.

$\frac{2}{3}$ of the number $=\frac{2}{3} \times x = \frac{2x}{3}$

Half of the number $=\frac{1}{2}\times x= \frac{x}{2}$

According to the question,

$\frac{2x}{3}= \frac{x}{2}+5$

$\frac{2x}{3} -\frac{x}{2} = 5$

$\frac{2x(2)-x(3)}{6}=5$           (LCM of 2 and 3 is 6)

$\frac{4x-3x}{6} = 5$

$\frac{x}{6}=5$

$x=5\times 6$

$x= 30$

So, the required number is 30. 

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Updated on: 10-Oct-2022

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