Answer: 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
