Question

The sum of two numbers is 18 and the sum of their reciprocals is `9/40`. Find the numbers.

Answer 1

Let the first number be x.

The sum of the two numbers is 18.

Second number = 18 − x

Now,

Sum of reciprocals = `9/40`

`1/x + 1/(18 − x)` = `9/40`

`(18 − x + x)/(x (18 − x))` = `9/40`

`18/(x (18 − x)` = `9/40`

`18 xx 40/9` = x(18 − x)

80 = 18x − x²

x² − 18x + 80 = 0

x² − 10x − 8x + 80 = 0

x(x − 10) − 8(x − 10) = 0

(x − 10) (x − 8) = 0

x − 10 = 0 or x − 8 = 0

x = 10 or x = 8

Hence, the two numbers are 8 and 10.