Question

Three consecutive odd integers are such that the sum of the first and second is 31 less than 3 times the third. Find the integers

Answer 1

n, n + 2, n + 4 - three consecutive odd integers

the sum of the first and second is 31 less than 3 times the third:

n + (n + 2) = 3(n + 4) - 31      use distributive property

n + n + 2 = (3)(n) + (3)(4) - 31

2n + 2 = 3n + 12 - 31

2n + 3 = 3n - 19       subtract 2 from both sides

2n = 3n - 21       subtract 3n from both sides

-n = -21        change the signs

n = 21

n + 2 = 21 + 2 = 23

n + 4 = 21 + 4 = 25

Answer: 21, 23, 25