Question 532452
One positive number is 2 more than twice another. If their product is 144, find the numbers.

The first sentence basically says: {{{x = 2y+2}}} (x is 2 more than twice y).
We also are told that the product of the 2 numbers is 144: {{{x*y = 144}}}.

Using substitution, x can be replaces with 2y + 2, to give us {{{(2y+2)*y = 144}}}.

We now solve this equation: {{{2y^2 + 2y = 144}}}.

Divide everything by 2: {{{y^2 + y = 72}}}.

Subtract 72 from both sides to get: {{{y^2 + y - 72 = 0}}}.

Factor the left side: {{{(y+9)*(y-8)=0}}}

So y=-9 or y=8. Since the question says the number is positive, we don't use -9.

So y = 8. Go back to the very first equation: x = 2y + 2. plug in 8 for y and we get x = 18. So the two numbers are 8 and 18.

You can check this by multiplying 8 and 18, to make sure you get 144.