# Math

posted by
**Lisa** on
.

LOL I can't figure this out. It should be easy it's been years since I've been in school and my son has no idea.

The product of two numbers is 63. Their sum is 16. What are the numbers?

Thanks for the help!

Let's factor 63.

1 x 63; 3 x 21; 7 x 9.

Which of those pairs of numbers adds up to 16?

If you want to do this all math, with no reasoning.

eqn 1: xy = 63

eqn 2: x+y=16

Solve for x and y.

=====================

solve for x from eqn 1.

x = 63/y

Plug this value into eqn 2 for x.

(63/y)+y=16

Multiply through by y

63 + y^2 = 16y

Rearrange

y^2 - 16y + 63 = 0

factor

(y-9)(y-7)=0

y=9 or 7

If y = 9, then

x=63/9=7 and the reverse is true.

So, y=9 and x=7 OR

y=7 and x=9

See, I didn't say this was an easier way to do it. It's an all math way of doing it. Reasoning it out is far simpler.

Good luck helping your son.

I THINK IT'S 7x9!