Question

If the sum and difference of two numbers is $35$ and $7$ respectively, find the product of the numbers?

Answer 1

Let the two numbers are $x$ and $y$

The sum of these two numbers is $35$

$x+y=35$ .................. (1)

The sum of these two numbers is $7$

$x-y=7$ .................. (2)

Adding Equation (1) and (2), we get,

$x+y+x-y=35+7$

$2x=42$

$x=\frac{42}{2}=21$

Substitute $x=21$ in equation (1)

$21+y=35$

$y=35-21$

$y=14$

So the two numbers are $21$ and $14$.

Hence Product=$294$