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.

Explanation

To solve the problem of finding three consecutive integers that, when multiplied by 2, 3, and 4 respectively, add up to 74, we can follow these steps:

### Step 1: Define the integers
Let the first consecutive integer be \( x \). Therefore, the three consecutive integers can be expressed as:
- First integer: \( x \)
- Second integer: \( x + 1 \)
- Third integer: \( x + 2 \)

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