Don't understand quadratic word problems at all. Please help, with steps.

Question

One number is 8 more than another number. Their product is 273. find the numbers.

The differance between a number and twice it's reciprocal is 17/10. What is the number?
Thanks,
Kelly

Answer 1

y = x + 8
x*y = 273

x*(x+8) = 273
x^2 + 8x - 273 = 0

(x-13)(x+21) = 0

One of those factors must evaluate to 0 for the answer to be 0. Therefore, x must equal either 13 or -21.

y must equal either 21 or -13.

So: x=13 and y=21
or x=-21 and y=-13

I'm sure you can figure out the second one.

Answer 2

For the first problem:
Let x = lesser number
let y = greater number
(x) (y) = 273
The problem states that y = x + 8.
substituting for y:
(x) (x+8)=273
x^2 + 8x=273
so
x^2 + 8x - 273 = 0
Solve for x.
Then, y = x + 8