Question

One number is three more than the other number. When the square of the smaller number is subtracted from the square of the smaller number, `45` is obtained. What are the two numbers?

Answer 1

Let the numbers be `x` and `y`.

`{(x + 3 = y), ((x + y)(y - x) = 45):}`

If we rearrange the first équation, we get `x - y = 3`. Substituting, we get:

`(x + (x + 3))(3) = 45`

`2x + 3 = 15`

`2x = 12`

`x = 6`

`:.`The numbers are `6` and `9`.

Hopefully this helps!

Answer 2

I got `6 and 9`

Explanation:

let s call our numbers `x` and `y`. We get:
`x=y+3`
and
`(x+y)(x-y)=45`
from the second we get:
`x^2-y^2=45`
substituting the first equation `x=y+3` we get:
`(y+3)^2-y^2=45`
`y^2+6y+9-y^2=45`
`6y=36`
`y=36/6=6`
so that `x=6+3=9`

Answer 3

The first number is 9, and the second number is 6.

Explanation:

Let `n` be the first number. The second number is therefore `n-3`.

Sum of the numbers: `color(red)((n)+(n-3) = 2n-3)`
Difference of the numbers: `color(blue)((n)-(n-3) = 3)`

Equation:
`color(red)((2n-3))color(blue)((3))=45`

`2n-3=15`

`2n=18`

`n=9` (First number)
`n-3=6` (Second number)