Question

Find three consecutive odd positive integers such that 3 times the sum of all three is 152 less than the product of the first and second integers

Answer 1

let the 3 cosecutive odd numbers be
x-2 , x, and x+2

3(x-2 + x + x+2) = x(x-2) - 152
9x = x^2 - 2x - 152
x^2 - 11x - 152 = 0

(x-19)(x + 8) = 0
x = 19, or x = -8 , but x is to be positive

the 3 numbers are:
17, 19, and 21

check:
their sum = 57
3 times their sum = 171

product of first and second = 17(19) = 323
Is 171 less than 323 by 152 ? YES

All is good