To find the missing number that makes the average of 42, 36, a missing value, and 25 equal to 30, follow these steps:
1. Determine the known values:
- We are given three numbers: 42, 36, and 25.
2. Calculate the total number of values:
- There are 4 numbers in total (including the missing one).
3. Calculate the target average:
- The target average is given as 30.
4. Calculate the required sum:
- To find the total sum that would give an average of 30 with 4 numbers, we use the formula for the average:
[tex]\[
\text{Average} = \frac{\text{Total Sum}}{\text{Number of Values}}
\][/tex]
- Rearranging this formula to find the Total Sum:
[tex]\[
\text{Total Sum} = \text{Average} \times \text{Number of Values}
\][/tex]
- Substituting the given values:
[tex]\[
\text{Total Sum} = 30 \times 4 = 120
\][/tex]
5. Calculate the sum of the known values:
- Add the known values: 42, 36, and 25.
[tex]\[
42 + 36 + 25 = 103
\][/tex]
6. Find the missing number:
- Subtract the sum of the known values from the required total sum:
[tex]\[
\text{Missing Number} = 120 - 103 = 17
\][/tex]
Therefore, the missing number is 17. So the complete set of numbers is 42, 36, 17, and 25, and their average is 30.
