Question
The mean of four numbers is 18 . If one of the four numbers is removed, the mean of the three remaining numbers is 17 . What is the value of the number that was removed?
Ask by Warren Hill. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The number removed is 21.
Solution
To find the value of the number that was removed, let's break down the problem step by step.
1. **Calculate the Total Sum of the Four Numbers:**
The mean of four numbers is given as 18. The mean is calculated by dividing the total sum of the numbers by the number of numbers. Therefore, the total sum (\( S_4 \)) of the four numbers is:
\[
S_4 = \text{Mean} \times \text{Number of items} = 18 \times 4 = 72
\]
2. **Calculate the Total Sum of the Remaining Three Numbers:**
After removing one number, the mean of the remaining three numbers is 17. Similarly, the total sum (\( S_3 \)) of these three numbers is:
\[
S_3 = \text{Mean} \times \text{Number of items} = 17 \times 3 = 51
\]
3. **Determine the Removed Number:**
The removed number (\( x \)) can be found by subtracting the sum of the remaining three numbers from the original total sum:
\[
x = S_4 - S_3 = 72 - 51 = 21
\]
**Answer:**
The number that was removed is **21**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find the number that was removed, we can start by using the information given about the means. The mean of the four numbers is 18, which means the total sum of the four numbers is: \[ 4 \times 18 = 72. \] When one of the numbers is removed, the mean of the remaining three numbers becomes 17, which means their total sum is: \[ 3 \times 17 = 51. \] Let \( x \) be the number that was removed. We can set up the equation: \[ 72 - x = 51. \] Now, solving for \( x \): \[ x = 72 - 51 = 21. \] So, the value of the number that was removed is 21.
