Answer
32
Work Step by Step
Let the unknown number be $x$. One-half of this number is $\frac{1}{2}x$ while three-fourths of this number is $\frac{3}{4}x$. Since the sum of one-half of the number and three-fourths of the number is 40, we write the following equation and solve:
$\frac{1}{2}x+\frac{3}{4}x=40$
$\frac{1x}{2}+\frac{3x}{4}=40$
$\frac{x(2)+3x}{4}=40$
$\frac{2x+3x}{4}=40$
$\frac{5x}{4}=40$
$5x=160$
$x=\frac{160}{5}=32$
Therefore, the unknown number is 32.
