The mean of three numbers is 30. If one of the numbers is 20, what is the mean o

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Question: The mean of three numbers is 30. If one of the numbers is 20, what is the mean of the other two numbers? (2023)

Options:

Correct Answer: 25

Exam Year: 2023

Solution:

Let the three numbers be a, b, c. Then, (a + b + 20) / 3 = 30. Thus, a + b = 90, and the mean of a and b = 90 / 2 = 45.

The mean of three numbers is 30. If one of the numbers is 20, what is the mean of the other two numbers? (2023)

The mean of three numbers is 30. If one of the numbers is 20, what is the mean of the other two numbers? (2023)

Step 1: Understand that the mean (average) of three numbers is given as 30.
Step 2: Recall that the mean is calculated by adding all the numbers together and dividing by the total count of numbers.
Step 3: Set up the equation for the mean: (a + b + 20) / 3 = 30, where a and b are the other two numbers.
Step 4: Multiply both sides of the equation by 3 to eliminate the fraction: a + b + 20 = 90.
Step 5: Subtract 20 from both sides to find the sum of a and b: a + b = 90 - 20 = 70.
Step 6: Now, to find the mean of a and b, divide their sum by 2: (a + b) / 2 = 70 / 2 = 35.

Mean Calculation – Understanding how to calculate the mean of a set of numbers and how to manipulate equations involving averages.
Algebraic Manipulation – Ability to rearrange and solve equations to isolate variables and find unknown values.