Question

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

Answer 1

Answer:

The numbers are 19 and 5

Step-by-step 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 $y = 5$

$y = -\frac{19}{2}$ 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