# word problem help

• Apr 13th 2008, 10:04 AM
gumi
word problem help
Find 2 numbers whose sum is 55 and whose product is 684 (show your work)

What are the dimension of a rectangle if it's perimeter is 18.5 and it's area is 21 (show your work)
• Apr 13th 2008, 10:15 AM
angel.white
Quote:

Originally Posted by gumi
Find 2 numbers whose sum is 55 and whose product is 684 (show your work)

Let A be the first number and B be the second number.

then A+B = 55 and A*B = 684

Solve for one variable
A = 55-B

Substitute it's value into the other equation so that you only have one variable in the other equation
(55-B)*B = 684

Set equal to zero so that quadratic formula can be used
-B^2 -55B -684 = 0

Use the quadratic formula The Quadratic Formula Explained to solve for B, and then plug that back into either equation to solve for A
• Apr 13th 2008, 10:28 AM
Moo
Hello,

We can also see that \$\displaystyle 684=2^2 . 3^2 . 19\$

A & B divide 684, so they divide 2².3².19 and their product is exactly 2².3².19

All possible couples are :

If a is the first factor, the second has to be 684/a as their product is 684
(1 , 684)
(2 , 2.3².19=342)
(3 , 2².3.19=226)
(4 , ...

Wait, wait ! This is too long to do !!!! :D

We know that A+B=55. So A & B are inferior to 55 ! Phew ! That reduces a lot the possibilities !
Actually, the only one for which the two factors are inferior to 55 is this one :

(2².3²=36 , 19) -> WOW their sum is 55 !

Did you understand how i got the couples ?
• Apr 13th 2008, 10:35 AM
angel.white
Quote:

Originally Posted by Moo
Did you understand how i got the couples ?

Yes, I just wasn't sure if the answer was going to have integers or even rational numbers as solutions.
• Apr 13th 2008, 10:39 AM
Moo
Actually, i had no worry that you would understand ^^ (and neither did i know :D)
I was just asking gumi :)
• Apr 13th 2008, 10:43 AM
gumi
got it guys thanks(Yes)