How to do it algerbically?

[EvoN1020v]

I can't figure out how to do this algerbically, though I know the answer:

 

There are 2 numbers that their sum is 100; and the product of the number is 24 times 100. The answers are 40 and 60.

 

I have 2 equations: [math]x + y = 100[/math] and [math]xy=2400[/math], but I'm not exactly sure how to put it together and get the answers. Can anybody help me?

[JustStuit]

Using [math]

x + y = 100

[/math] and [math]

xy = 2400

[/math] set one equal to y or x (I'll choose first one for y) and you get [math]

y = 100 -x

[/math] then plug that into second to get [math]

y (100-y) = 2400

[/math]. Using quadratic [math]

(100 +/- (10000-4(1)(2400))^(1/2))/2

[/math] to get [math]

40 or 60

[/math] then plug those into first to get [math]

x = 100-40

[/math] or [math]

x = 100-60

[/math] which is also 60 or 40

[JustStuit]

Excuse my latex I'm not too good at it

[EvoN1020v]

Right, I got it. You used the method of substitution.

[JustStuit]

I guess that would have been a simplier explanation lol

[EvoN1020v]

Ok JustStuit, I'll fix your Latex mistakes, so other people can read the solution.

 

The quadratic equation is: [math]x^{2} - 100x + 2400[/math]

 

Using the quadratic formula: [math]\frac{-100 \pm \sqrt{10,000 - 4(1)(2400)}}{2}[/math]

 

It will yield: [math]50 \pm 10[/math] Therefore [math]40[/math] and [math] 60.[/math]