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I need help solving a complicated fraction.

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by STI-R » Wed Oct 16, 2013 8:16 pm
1/f + 1/1.25f = 1/5
f=?

This is a problem directly from the purple math website. I can't for the life of me isolate "f". Could someone kindly show step by step on how to solve for f? I already know what the answer is, I just want someone to show me how to get the f. Thanks to whoever solves my problem.
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by mevicks » Wed Oct 16, 2013 8:38 pm
1/f + 1/(1.25f) = 1/5

Multiply and divide 1/f by 1.25
1.25/1.25f + 1/1.25f = 1/5

Denominators of LHS are same so club them
(1.25 + 1) / 1.25f = 1/5
2.25 / 1.25f = 1/5

Cross multiply
f = (2.25 /1.25) * 5

Multiply and divide (2.25 /1.25) by 100 to simplify the calculations
f = (225/125) * 5
f = 9

Hope it helps.
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by STI-R » Wed Oct 16, 2013 8:53 pm
Thank you so much!
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by [email protected] » Wed Oct 16, 2013 9:48 pm
Hi STI-R,

Here's another way to solve for F:

1/F + 1/(1.25F) = 1/5

Multiply everything by F:

F/F + F/(1.25F) = F/5

Simplify:

1 + 4/5 = F/5

1.8 = F/5

1.8(5) = F

9 = F

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