Intelligent Math Puzzle – Challenge 92

Challenge:

If A and B are integers and \(\frac{1}{B}=\frac{1}{A}-\frac{1}{20}\) what is the value of A+B?

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\(\frac{1}{B} =\frac{1}{A} -\frac{ 1}{20}\)
Therefore, A is less than B. Why?
Plug in different values for A.
Let’s begin with 2. If A \(= 2 → \frac{1}{B} = \frac{ 1}{2} – \frac{ 1}{20} → \frac{ 1}{B} = \frac{ 9}{20} → 9B = 20\)
B is an integer. Therefore, B cannot be \(\frac{ 20}{9}\)
A \(= 3 → \frac{ 1}{B} = \frac{ 1}{3} – \frac{ 1}{20} → \frac{ 1}{B} = \frac{ 17}{60} → 17B = 60\)
A \(= 4 → \frac{ 1}{B} = \frac{ 1}{4} – \frac{ 1}{20} → \frac{ 1}{B} = \frac{4}{20} → 4B = 20 → B = 5\) Bingo!
A = 4 and B = 5 → A + B = 9

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