Algebra
posted by Kelly on .
Don't understand quadratic word problems at all. Please help, with steps.
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

y = x + 8
x*y = 273
x*(x+8) = 273
x^2 + 8x  273 = 0
(x13)(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. 
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