The average of three consecutive integers is 20. What is the smallest of these i

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

Options:

Correct Answer: 18

Exam Year: 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.

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

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

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.

Average of Consecutive Integers – Understanding how to calculate the average of a set of consecutive integers and how to set up equations based on that average.
Algebraic Manipulation – Solving linear equations to find the value of a variable representing the smallest integer.