Question

the sum of a negative number, 1/4 of the negative number, and 7/16 of the negative number is – 13 1/2 . What is the negative number?

Answer 1

the negative number is -8

Explanation:

let the negative number = y

1/4 of the negative number = 1/4 (y) = y/4

7/16 of the negative number = 7/16 (y) = 7y/16

sum of the three numbers = -13 1/2

Adding all three numbers:

$\begin{gathered} \text{negative number + 1/4 of the negative number + 7/16 of the negative number} \\ y\text{ + }\frac{y}{4}\text{ + }\frac{7y}{16} \\ \\ y\text{ + }\frac{y}{4}\text{ + }\frac{7y}{16}\text{ = given sum} \\ y\text{ + }\frac{y}{4}\text{ + }\frac{7y}{16}\text{ = -13}\frac{1}{2} \\ y\text{ + }\frac{y}{4}\text{ + }\frac{7y}{16}\text{ = }\frac{-27}{2} \\ \end{gathered}$$\begin{gathered} \text{LCM: 16} \\ \frac{16(y)\text{ + 4(y) + 1(7y)}}{16}\text{ = }\frac{-27}{2} \\ \frac{16y\text{ + 4y+ 7y}}{16}\text{ = }\frac{-27}{2} \\ \frac{2\text{7y}}{16}\text{ = }\frac{-27}{2} \end{gathered}$$\begin{gathered} \text{cross multiply:} \\ 2(27y)\text{ = 16(-27)} \\ 54y\text{ = }-432 \\ \\ \text{Divide both sides by 54:} \\ y\text{ = }\frac{-432}{54} \\ y\text{ = }-8 \end{gathered}$

Hence, the negative number is -8