Question

Find two consecutive odd integers such that 3 times the lesser added to the greater gives a sum of 126.

a. 25, 27
b. 27, 29
c. 29, 31
d. 31, 33

Answer 1

The two consecutive odd integers where three times the lesser added to the greater equals 126 are 31 and 33. We find these by setting up an equation 3x + (x + 2) = 126 and solving for x.

Step-by-step explanation:

To find two consecutive odd integers where 3 times the lesser added to the greater equals 126, we can let the first odd integer be x, and the next consecutive odd integer would be x+2 (since odd numbers are two units apart).

The equation based on the given conditions would be 3x + (x + 2) = 126. Simplifying the equation, we combine like terms to get 4x + 2 = 126.

To solve for x, we then subtract 2 from both sides to get 4x = 124 and divide by 4 to find x, giving us x = 31. Accordingly, the two consecutive odd integers are 31 and 31+2, which is 33. The correct answer is option d: 31, 33.