Posted by **Lisa** on Wednesday, January 17, 2007 at 4:46pm.

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!

## Answer this Question

## Related Questions

- math - Two rational numbers with the sum of 1, product of -6/25 and quotient of...
- math - the difference of two numbers is 5. their product is 176. what are the ...
- medical billing and coding from Penn Foster - I am writing a research paper for ...
- Math - What do you call numbers that cannot be arranged into 2-row arrays? ...
- math - Find the two numbers that multiply to the product number and add to the ...
- algebra - the sum of two numbers is 21. The first number is 2/5 of the second ...
- Int Algebra - The difference of two numbers is 7. The sum of the numbers is -1. ...
- Math - I'm sorry it's been a while since I've been on Jishka. how are you guys? ...
- 4th Grade Math - Re: Factor Numbers My son has to write at least two ways to ...
- 4th Grade Math - Re: Factor Numbers My son has to write at least two ways to ...

More Related Questions