SOLUTION: On my Precal 20 test there was this question: Two numbers equal 32. Their reciprocals equal 1/6. What are the two numbers? I came up with two equations: X+Y=32 and of course 1/X

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: On my Precal 20 test there was this question: Two numbers equal 32. Their reciprocals equal 1/6. What are the two numbers? I came up with two equations: X+Y=32 and of course 1/X      Log On


   

Question 813468: On my Precal 20 test there was this question:
Two numbers equal 32. Their reciprocals equal 1/6. What are the two numbers?
I came up with two equations:
X+Y=32 and of course 1/X+1/Y=1/6 but no matter what I do the question seems impossible.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x + y = 32

y = 32 - x

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1/x + 1/y = 1/6

1/x + 1/(32 - x) = 1/6

6x(32-x) * [1/x + 1/(32 - x)] = 6x(32-x)*(1/6) ... multiply both sides by the LCD to clear out the fractions

6(32-x) + 6x = x(32-x)

192 - 6x + 6x = 32x - x^2

192 = 32x - x^2

0 = 32x - x^2 - 192

32x - x^2 - 192 = 0

-x^2 + 32x - 192 = 0

-1*(-x^2 + 32x - 192) = -1*0

x^2 - 32x + 192 = 0

(x-8)(x-24) = 0

I'll let you finish up. Don't forget to check any possible answers you get.