## Elementary Algebra

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.