Math

posted by .

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.

I THINK IT'S 7x9!

Similar Questions

1. Math

What do you call numbers that cannot be arranged into 2-row arrays?
2. Int Algebra

The difference of two numbers is 7. The sum of the numbers is -1. What are the numbers?
3. maths

the sum of N positive integers is 19. what is the maximum possible product of these N numbers?
4. Math

When factoring a trinomial that is in the format Ax^2 + Bx + C, the number that is represented by B should be viewed as the _____?
5. math

Two rational numbers with the sum of 1, product of -6/25 and quotient of -6. ( I have been working on this for a long time but I can't figure it out!)

Re: Factor Numbers My son has to write at least two ways to break down numbers - I know he did not learn this in school but I would like to help him at home, please help me I have not done this work in over 30 years. He has to break …