Answer:
The numbers are 19 and 5
Step-by-step explanation:
Given
Let the numbers be [tex]x\ and\ y.[/tex]
So:
[tex]x = 9 + 2y[/tex] --- First statement
[tex]x*y = 95[/tex] --- second statement
Required
Find x and y
Substitute [tex]x = 9 + 2y[/tex] in [tex]x*y = 95[/tex]
[tex](9 + 2y) * y = 95[/tex]
[tex]9y + 2y^2 = 95[/tex]
Rewrite as:
[tex]2y^2 + 9y - 95 = 0[/tex]
Expand
[tex]2y^2 -10y +19y- 95 = 0[/tex]
Factorize
[tex]2y(y -5) +19(y- 5) = 0[/tex]
[tex](2y +19)(y- 5) = 0[/tex]
Solve for y
[tex]2y + 19 =0[/tex] or [tex]y - 5 = 0[/tex]
[tex]2y = -19[/tex] or [tex]y = 5[/tex]
[tex]y = -\frac{19}{2}[/tex] or [tex]y=5[/tex]
Since the numbers are positive, we take only:
[tex]y=5[/tex]
Substitute [tex]y=5[/tex] in [tex]x = 9 + 2y[/tex]
[tex]x = 9 + 2 * 5[/tex]
[tex]x = 9 + 10[/tex]
[tex]x = 19[/tex]
The numbers are 19 and 5
