Question

The sum of two numbers a and b is 15, and the sum of their reciprocals is 3/10. Find the numbers a and b.

Answer 1

Numbers a and b are 5 and 10.

Step-by-step explanation:

Let the two numbers be x and 15-x, then we get:

1/x + 1/(15-x) = 3/10

10 (15 - x + x ) = 3(x(15-x)

150 = 3x (15 -x )

50 = 15x - x²

x² - 15x + 50 = 0

Factors of +50 are -10 and -5.

So  x² - 15x + 50 = 0 can be written as:

 x² -10x -5x + 50 = 0

 x (x -10) -5 (x -10) = 0

(x -10) (x -5) = 0

So the factors are (x - 5) and (x - 10).

If x - 5 = 0, then x = 5

If x - 10 = 0, then x = 10

Hence solved.

X = 5, 10