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

Step-by-step 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{ + }(y)/(4)\text{ + }(7y)/(16) \\ \\ y\text{ + }(y)/(4)\text{ + }(7y)/(16)\text{ = given sum} \\ y\text{ + }(y)/(4)\text{ + }(7y)/(16)\text{ = -13}(1)/(2) \\ y\text{ + }(y)/(4)\text{ + }(7y)/(16)\text{ = }(-27)/(2) \\ \end{gathered}`
`\begin{gathered} \text{LCM: 16} \\ \frac{16(y)\text{ + 4(y) + 1(7y)}}{16}\text{ = }(-27)/(2) \\ \frac{16y\text{ + 4y+ 7y}}{16}\text{ = }(-27)/(2) \\ \frac{2\text{7y}}{16}\text{ = }(-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{ = }(-432)/(54) \\ y\text{ = }-8 \end{gathered}`

Hence, the negative number is -8