SOLUTION: If 1/a + 1/b = 5/12 and ab = 24, what is the value of a+b?

Question 1209283: If 1/a + 1/b = 5/12 and ab = 24, what is the value of a+b?
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

There are at least three ways to answer this question.

Method 1

Plug in ab = 24.

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Method 2

Multiply both sides by ab

Distribute

Plug in ab = 24

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Method 3

ab = 24 rearranges to b = 24/a which has reciprocal 1/b = a/24

Then,

Replaced 1/b with a/24

Multiply both sides by the LCD 24a to clear out the fractions.

or

or

If a = 6, then b = 24/a = 24/6 = 4.
If a = 4, then b = 24/a = 24/4 = 6.
The order of a,b doesn't matter so we arrive at the same pairing.

The pair of values is a = 4 and b = 6 (or a = 6 and b = 4).
As a way to check,

In short which helps us confirm we have the correct a,b values.

Then a+b = 4+6 = 10

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Answer: 10

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