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

5 and 10

Step-by-step explanation:

Let the first number be denoted as y

Then the second number will be y/15.

Since the sum of their reciprocal is 3/10, therefore:

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

Using LCM will result into:

15/(15y - y²) = 3/10

We then cross multiply

150 = 3(15y - y²)

150 = 45y - 3y²

3y² - 45y + 150 = 0

Divide through by 3

y² - 15y + 50 = 0

y² - 5y - 10y + 50 = 0

(y - 10)(y - 5) = 0

Therefore,

y - 10 = 0 or y - 5 = 0

y = 0 + 10 or y = 0 + 5

y = 10 or y = 5

Therefore the numbers are 5 and 10

24 units

step-by-step explanation: