Find the 3 consecutive numbers whose product divided by each of them, the sum of the 3 quotients is 74?

Question

If the product of 3 consecutive numbers is divided by each of them in turn, the sum of the 3 quotients will be 74.
What are the numbers?

Answer 1

Let's say the 3 consecutive numbers are x, y and z. ( x = y - 1, z = y + 1)
xyz/x + xyz/y + xyz/z = 74
yz + xz + xy = 74
y(y + 1) + (y -1)(y + 1) + y(y - 1) = 74
(y² + y) + (y² - 1) + y² - y = 74
3y² - 1 = 74
3y² = 75
y² = 25
∴ y = 5 , x = 4 , z = 6

The 3 consecutive numbers are 4, 5 and 6.

Comments

Excellent.