Hi Lisa,

Here is a similar problem that will show you how to approach your problems.

Two positive numbers differ by 4. Their product is 165. What are the two numbers?

There are two unknown numbers so let one be x and the other y. The two facts then become

Two positive numbers differ by 4: x - y = 4
Their product is 165: xy = 165

You want one equation in one unknown and you have two equations in two unknowns.

Since x - y = 4 adding y to both sides gives x = y + 4. Substitute this into the second equation to get

(y + 4)y = 165

which simplifies to

y² + 4y - 165 = 0

The challenge is then to factor this quadratic. A little experimentation with the divisors of 165 gives me

y² + 4y - 165 = (y + 15)(y - 11)

Thus y² + 4y - 165 = 0 has solutions y = 11 and y = -15. Since we want y to be positive we have y = 11. Now from the first equation, x - y = 4, if y = 11 then x must be 15. Hence the two numbers are 11 and 15.

Now try your problems,
Penny