Four times the greatest of three consecutive odd integers exceeds three times the least by 31. What is the greatest of the three consecutive odd integers?

Explanation

To solve the problem, express the three consecutive odd integers as x, x + 2, and x + 4. The problem states that four times the greatest integer (x + 4) exceeds three times the least integer (x) by 31, giving the equation: 4(x + 4) = 3x + 31.Solving for x results in x = 15. Therefore, the greatest of the three integers is x + 4 = 19. Options 33, 47, and 61 do not satisfy the equation and lead to non-integer solutions for x, making them incorrect choices.