. How many positive integers satisfy the equation, 3/x - 4/y = 1
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Answer:
3x + 4y = 120
120 is an even integer.
y = 120/4 - 3x/4 = 30 - 3x/4
As y is an even integer. So, the condition on x is that it must be a multiple of 4. And maximum value of x is 40. So, the possible values of x is 4, 8, 12, 16, 20, 24, 28, 32, 36. (x can't be 40. Because if x =40 then y =0 and it is not possible)
Let's check few possibilities.
When x = 4
4y = 108 => y = 108/4 = 27
When x = 8
4y = 96 => y = 96/4 = 24
When x = 12
4y = 84 => y = 84/4 = 21
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