Question

7. The sum of two integers is 41. The difference between the two integersis 7. What is the smaller number?}-C. 24A 14D. 27B. 17

Answer 1

Let the two intgers be x and y.

Their sum is 41

`x+y=41`

Their difference is 7, so

`x-y=7`

Making x the subject in equation 1, we have

`\begin{gathered} x+y=41 \\ y=41-x \end{gathered}`

Substitute y for 41 - x into equation 2, we have

`\begin{gathered} x-y=7 \\ x-(41-x)=7 \\ x-41+x=7 \\ collecting\text{ like terms} \\ x+x=41+7 \\ 2x=48 \\ x=(48)/(2) \\ x=24 \end{gathered}`

From y = 41 - x, we have

`\begin{gathered} y=41-x \\ y=41-24 \\ y=17 \end{gathered}`

Hence the smaller number is 17