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

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

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

Steps: 9

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.