Mathematics
posted by Mandy on .
The difference between two numbers is 9 and the product of the numbers is 162. Find the two numbers. Explain your working

Let x be the larger number
x*(x9) = 162
Rearrange and factor
x^2  9x 162 = 0
(x+9)(x  18) = 0
Take it from there.
There will be two pairs of solutions. 
By symbols
AB=9
AxB=162
so A=9+B
(9+B)B=162
9B+B^2=162
B^2+9B162=0
so B=18 or 9
correspondingly from AxB=162
A=9 or 18
check against AB=9
918=9
189=9