The average of three consecutive integers is 20. What is the largest of these in

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

Options:

Correct Answer: 21

Solution:

Let the integers be x, x+1, x+2. Average = (x + (x+1) + (x+2)) / 3 = 20. Solving gives x = 19, largest integer = 21.

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

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

Correct Answer: 21

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: Now, we divide the total by 3 to find the average: (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 by 3 to solve for x: x = 19.
Step 10: Now, find the largest integer, which is x + 2: 19 + 2 = 21.

Average of Consecutive Integers – Understanding how to calculate the average of a set of consecutive integers and how to represent them algebraically.
Algebraic Manipulation – Solving equations involving variables to find specific integer values.