Question

One positive number is 9 more than twice another. If their product is 95, find the numbers.

Answer 1

The numbers are 19 and 5

Explanation:

Given

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

So:

`x = 9 + 2y` --- First statement

`x*y = 95` --- second statement

Required

Find x and y

Substitute
`x = 9 + 2y` in
`x*y = 95`

`(9 + 2y) * y = 95`

`9y + 2y^2 = 95`

Rewrite as:

`2y^2 + 9y - 95 = 0`

Expand

`2y^2 -10y +19y- 95 = 0`

Factorize

`2y(y -5) +19(y- 5) = 0`

`(2y +19)(y- 5) = 0`

Solve for y

`2y + 19 =0` or
`y - 5 = 0`

`2y = -19` or
`y = 5`

`y = -(19)/(2)` or
`y=5`

Since the numbers are positive, we take only:

`y=5`

Substitute
`y=5` in
`x = 9 + 2y`

`x = 9 + 2 * 5`

`x = 9 + 10`

`x = 19`

The numbers are 19 and 5