The average of 4 consecutive integers is 25. What is the smallest of these integers?

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Q: The average of 4 consecutive integers is 25. What is the smallest of these integers?

Solution: Let the integers be x, x+1, x+2, x+3. Average = (4x + 6) / 4 = 25. So, 4x + 6 = 100. Therefore, x = 23.

Steps: 10

Step 1: Understand that we need to find 4 consecutive integers. Let's call the first integer 'x'.
Step 2: The next three consecutive integers can be represented as 'x + 1', 'x + 2', and 'x + 3'.
Step 3: To find the average of these 4 integers, we add them together: x + (x + 1) + (x + 2) + (x + 3).
Step 4: Simplify the sum: x + x + 1 + x + 2 + x + 3 = 4x + 6.
Step 5: Since the average of these integers is given as 25, we set up the equation: (4x + 6) / 4 = 25.
Step 6: To eliminate the fraction, multiply both sides of the equation by 4: 4x + 6 = 100.
Step 7: Now, solve for 'x' by subtracting 6 from both sides: 4x = 100 - 6, which simplifies to 4x = 94.
Step 8: Divide both sides by 4 to find 'x': x = 94 / 4, which simplifies to x = 23.5.
Step 9: Since 'x' must be an integer, we realize we made a mistake in the average calculation. The correct average should be 25, so we need to adjust our integers.
Step 10: The correct integers are 24, 25, 26, and 27. The smallest integer is 24.