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Question 23
The sum of two integers is 10 and the sum of their reciprocals is 5/12. Then the larger of these integers is
Solution
let's say integers are x and y
so x+y = 10 => y = 10 - x
and $$\frac{1}{x} + \frac{1}{y} = \frac{5}{12}$$
$$\frac{1}{x} + \frac{1}{10-x} = \frac{5}{12}$$
=> (10 - x + x)*12 = 5*x(10-x)
=> $$120 = 50x - 5x^2$$
=> $$24 = 10x - x^2$$
=> x = 4, 6
=> y = 6 or 4
The bigger of the two numbers is 6.
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