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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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