Question

A positive integer is 5more than 23 times another. Their product is 6732. Find the two integers

Answer 1

One integer is m.

The other integer is n.

n = 23m + 5

mn = 6732

m = 6732/n

n = 23 * 6732/n + 5

n = 154,836/n + 5

n^2 = 154,836 + 5n

n^2 - 5n - 154,836 = 0

n = [5 +- sqrt(25 + 4 * 154,836)]/2

n = (5 +- 787)/2

n = 396 or n = -391

We discard -391 because the problem is looking for positive integers.

mn = 6732

m = 6732/n = 6732/396

m = 17

Answer: The integers are 17 and 396.