Question

6. If one number is 6 more than another and the difference of their squares is 144, what are the

numbers?

Answer 1

Explanation:

Let x be the first number and x + 6 be the second

So we have...

`{(x + 6)}^(2) - {x}^(2) = 144`

Expand and rearrange:

`{x}^(2) + 12x + 36 - {x}^(2) - 144 = 0`

Simplify:

`12x + 36 = 144`

Subtract 36 from each side:

`12x =108`

Divide both sides by 12:

`x = 9`

9 is the First Number

And so we can conclude that:

`x + 6 = 15`

15 is the Second Number

Hope this helps!!