The average of three numbers is 1/5. Two of the numbers are 1/4 and 1/3. what is the third number?

The third number is 1/60

Step-by-step explanation:

Let the denominator of the number = x

1/4 + 1/3 + 1/x = 1/5

1/4 + 1/3 = 3/12 + 4/12 = 7/12

The lowest common denominator is 60x.

(7/12 + 1/x)/3 = 1/5        Remember that this is the average of 3 numbers. That's what the 3 is doing on the left. Multiply both sides by 3

7/12 + 1/x = 3/5            Multiply through by 60x

35x + 60 = 36x

x = 60

Very nice problem. Thanks for posting.  This problem is a little involved. If you have trouble with it, leave a note in the comments and I'll come back and discuss it.

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