The average of three consecutive integers is 20. What are the integers?

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Question: The average of three consecutive integers is 20. What are the integers?

Options:

Correct Answer: 19, 20, 21

Solution:

Let the integers be x, x+1, x+2. (x + (x + 1) + (x + 2)) / 3 = 20. Therefore, 3x + 3 = 60, so x = 19.

The average of three consecutive integers is 20. What are the integers?

The average of three consecutive integers is 20. What are the integers?

Step 1: Understand that we are looking for three consecutive integers. Let's call the first integer 'x'.
Step 2: The next two consecutive integers can be expressed 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: The average is found by dividing the total by 3: (3x + 3) / 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: Now, find the three consecutive integers: 19, 20, and 21.

Average of Consecutive Integers – Understanding how to calculate the average of a set of numbers, particularly consecutive integers.
Algebraic Representation – Using variables to represent unknown quantities and forming equations based on given conditions.
Solving Linear Equations – Applying algebraic methods to solve for the variable in a linear equation.