The mean of five consecutive integers is 12. What is the smallest of these integ

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Question: The mean of five consecutive integers is 12. What is the smallest of these integers?

Options:

Correct Answer: 10

Solution:

Let the integers be x, x+1, x+2, x+3, x+4. Mean = (5x + 10) / 5 = 12. Solving gives x = 10.

The mean of five consecutive integers is 12. What is the smallest of these integers?

The mean of five consecutive integers is 12. What is the smallest of these integers?

Step 1: Understand that we are looking for five consecutive integers. Let's call the smallest integer 'x'.
Step 2: The five consecutive integers can be represented as: x, x+1, x+2, x+3, x+4.
Step 3: To find the mean (average) of these integers, we add them together: x + (x+1) + (x+2) + (x+3) + (x+4).
Step 4: Simplify the sum: x + x + 1 + x + 2 + x + 3 + x + 4 = 5x + 10.
Step 5: Since the mean is given as 12, we set up the equation: (5x + 10) / 5 = 12.
Step 6: Multiply both sides of the equation by 5 to eliminate the fraction: 5x + 10 = 60.
Step 7: Subtract 10 from both sides: 5x = 50.
Step 8: Divide both sides by 5 to solve for x: x = 10.
Step 9: The smallest of the five consecutive integers is x, which is 10.

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