Question
Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.
Solution
Let the integers be x, (x+1) and (x+2).
∴ According to the condition, we have
or 2x + 3x +3 + 4x + 8 =74
or 9x +11 = 74
or 9x = 74 - 11 = 63
Dividing both sides by 9, we have
x = 63
9 = 7
∴ The required integers are:
7, (7+1) and (7+2) or 7, 8, and 9.
