Question

the product of two numbers is 100. if one decreased by 5 and the other increased by 1, the product is still 100. how do i find the numbers?

Answer 1

Let the two numbers be \(x\) and \(y\)

Answer 2

Can you set up equations based on given info ?

Answer 3

xy= 100
(x-5)(y+1)=100
I'm not sure where to go from there. I set them equal to each other, but that didn't work

Answer 4

Your equations look good. Try eliminating one variable by substitution

Answer 5

\(xy= 100 \implies y = 100/x\)

plug this in second equation

Answer 6

\((x-5)(\frac{100}{x}+1)=100\)

Answer 7

\((x-5)(\frac{100+x}{x})=100\)

Answer 8

\((x-5)(100+x)=100x\)

Answer 9

expand the left hand side
you will see a quadratic equation which can be solved using quadratic formula

Answer 10

x=-20 or x= 25. I understand it now. Thanks!

Does the equation also work if I substitute it after I expand the binomials?

Answer 11

I see that it does work. I did that in the beginning but I made an error somewhere, so I couldn't solve it.
Thanks again.

Answer 12

np :)