Question

The sum of two numbers is $95$. If one exceeds the other by $15$, find the numbers.

Answer 1

Finding two numbers such that their sum is $95$ and one number exceeds the other number by $15$:

Let one of the number be $\mathrm{x}$.

Then the other number becomes $\mathrm{x}+15$.

According to the question,

Sum of the two numbers $=95$

$$\begin{gathered} \Rightarrow \mathrm{x}+\left(\mathrm{x}+15\right)=95 \\ \Rightarrow 2\mathrm{x}+15=95 \\ \Rightarrow 2\mathrm{x}=95-15 \\ \Rightarrow 2\mathrm{x}=80 \\ \Rightarrow \mathrm{x}=\frac{80}{2} \\ \Rightarrow \mathrm{x}=40 \end{gathered}$$

Thus one number is $\mathrm{x}=40$,

Another number is $\mathrm{x}+15=40+15=55$.

Therefore the required numbers are $40$ and $55$.