Question

When 2/3 of a number is increased by 20, the sum is then halved, the result obtained is the same as 2/3 of the number, increased by 3. Find the number.

Answer 1

$\frac{2/3x+20}{2} =\frac{2}{3} x+3\\\frac{2/3x+20}{2} - 3 = \frac{2}{3}x\\\frac{2/3x+20}{2} - \frac{6}{2} = \frac{2}{3}x\\\frac{2/3x+20-6}{2} = \frac{2}{3}x\\\frac{2/3x+14}{2} = \frac{2}{3}x\\2(\frac{2/3x+14}{2}) = 2(\frac{2}{3}x)\\2/3x+14=\frac{4}{3}x\\14=\frac{4}{3}x-\frac{2}{3}x\\14=\frac{2}{3}x\\\frac{14}{1}/\frac{2}{3}=x\\\frac{14}{1}*\frac{3}{2}=x\\7*3=x\\x=21$

The number is 21.