The average of three consecutive integers is 20. What is the smallest of these integers? (2023)

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Q: The average of three consecutive integers is 20. What is the smallest of these integers? (2023)

Solution: Let the integers be x, x+1, x+2. The average is (x + (x + 1) + (x + 2)) / 3 = 20. Solving gives x = 18.

Steps: 10

Step 1: Understand that we are looking for three consecutive integers. Let's call the smallest integer 'x'.
Step 2: The next two consecutive integers can be represented as 'x + 1' and 'x + 2'.
Step 3: To find the average of these three integers, we add them together: x + (x + 1) + (x + 2).
Step 4: Simplify the sum: x + x + 1 + x + 2 = 3x + 3.
Step 5: Now, we need to find the average, which is (3x + 3) divided by 3.
Step 6: Set the average equal to 20: (3x + 3) / 3 = 20.
Step 7: Multiply both sides by 3 to eliminate the fraction: 3x + 3 = 60.
Step 8: Subtract 3 from both sides: 3x = 57.
Step 9: Divide both sides by 3 to solve for x: x = 19.
Step 10: Since we are looking for the smallest integer, the answer is x, which is 19.