Question

Sum of two numbers is $95$. If one exceeds the other by $3$, find product of the numbers.

Answer 1

Let the one number be $x$ and the other number be $y$.

It is given that the sum of the numbers is $95$,
therefore, we have: $x+y=95....\left(1\right)$

It is also given that one number exceeds the other by $3$ which means:

$x=y+3\Rightarrow x-y=3....\left(2\right)$

Now, we add equations 1 and 2 as follows:

$x+y+x-y=95+3\Rightarrow (x+x)+(y-y)=98\Rightarrow 2x=98\Rightarrow x=\frac{98}{2}\Rightarrow x=49$

Now, substitute the value of $x$ in equation (2) to find the value of $y$ as shown below:

$x-y=3\Rightarrow 49-y=3\Rightarrow y=49-3\Rightarrow y=46$

Therefore, the two numbers are $x=49$ and $y=46$ and the product of the numbers is: $x\times y=49\times 46=2254$.

Hence, the product of the numbers is $2254$.