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December 21, 2014

December 21, 2014

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

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!

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