The mean of three numbers is 15. If one of the numbers is 10, what is the mean o

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Question: The mean of three numbers is 15. If one of the numbers is 10, what is the mean of the other two numbers? (2020)

Options:

Correct Answer: 20

Exam Year: 2020

Solution:

Let the other two numbers be a and b. Then, (10 + a + b) / 3 = 15. Solving gives (a + b) = 35, so Mean of a and b = 35 / 2 = 17.5.

The mean of three numbers is 15. If one of the numbers is 10, what is the mean of the other two numbers? (2020)

The mean of three numbers is 15. If one of the numbers is 10, what is the mean of the other two numbers? (2020)

Step 1: Understand that the mean (average) of three numbers is calculated by adding the numbers together and dividing by the total count of numbers, which is 3 in this case.
Step 2: We know the mean of the three numbers is 15. This means that if we add all three numbers together and divide by 3, we should get 15.
Step 3: Let the three numbers be 10, a, and b. We can write the equation: (10 + a + b) / 3 = 15.
Step 4: To eliminate the division, multiply both sides of the equation by 3: 10 + a + b = 15 * 3.
Step 5: Calculate 15 * 3, which equals 45. So now we have: 10 + a + b = 45.
Step 6: To find a + b, subtract 10 from both sides: a + b = 45 - 10.
Step 7: Calculate 45 - 10, which equals 35. So now we have: a + b = 35.
Step 8: To find the mean of the two numbers a and b, we use the formula: Mean of a and b = (a + b) / 2.
Step 9: Substitute a + b with 35: Mean of a and b = 35 / 2.
Step 10: Calculate 35 / 2, which equals 17.5. Therefore, the mean of the other two numbers is 17.5.

Mean Calculation – Understanding how to calculate the mean of a set of numbers and how to manipulate equations involving averages.
Algebraic Manipulation – Ability to set up and solve equations based on given information.