SOLUTION: How would I set up this word problem? "The sum of a number and its reciprocal is 29/10. Find the number." The eguation that I have tried looks like this:

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: How would I set up this word problem? "The sum of a number and its reciprocal is 29/10. Find the number." The eguation that I have tried looks like this:       Log On


   

Question 582084: How would I set up this word problem?
"The sum of a number and its reciprocal is 29/10. Find the number."
The eguation that I have tried looks like this:
x + 1/x=29/10
By the way the 1/x, for example, represents 1 over x.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
x + 1%2Fx = 29%2F10, just like you have it
multiply thru by 10x, cancel the denominators and you have:
10x(x) + 10 = 29x
10x^2 - 29x + 10 = 0; a quadratic equation
Use the quadratic formula, but this will factor to
(5x - 2)(2x - 5) = 0
two solutions
5x = 2
x = 2%2F5
and
2x = 5
x = 5%2F2, note they are the reciprocal of each other
:
:
Check with x =2%2F5
2%2F5 + 5%2F2 =
4%2F10 + 25%2F10 = 29%2F10