Answer :
Sure! Let's solve this step-by-step.
To find the unknown fourth number, let's follow these steps:
1. We know that the mean (average) of four numbers is 71.5.
2. The formula for the mean (average) is given by:
[tex]\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}
\][/tex]
3. Rearranging this formula to find the sum of all values, we get:
[tex]\[
\text{Sum of all values} = \text{Mean} \times \text{Number of values}
\][/tex]
4. Plugging in the known values:
[tex]\[
\text{Sum of all values} = 71.5 \times 4 = 286
\][/tex]
5. Now, we know three of the numbers: 58, 76, and 88. Let's calculate their sum:
[tex]\[
58 + 76 + 88 = 222
\][/tex]
6. To find the fourth number, we subtract the sum of the known three numbers from the total sum of all four numbers:
[tex]\[
\text{Fourth number} = 286 - 222 = 64
\][/tex]
7. Therefore, the value of the fourth number is 64.
Hence, the correct answer is:
a. 64
To find the unknown fourth number, let's follow these steps:
1. We know that the mean (average) of four numbers is 71.5.
2. The formula for the mean (average) is given by:
[tex]\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}
\][/tex]
3. Rearranging this formula to find the sum of all values, we get:
[tex]\[
\text{Sum of all values} = \text{Mean} \times \text{Number of values}
\][/tex]
4. Plugging in the known values:
[tex]\[
\text{Sum of all values} = 71.5 \times 4 = 286
\][/tex]
5. Now, we know three of the numbers: 58, 76, and 88. Let's calculate their sum:
[tex]\[
58 + 76 + 88 = 222
\][/tex]
6. To find the fourth number, we subtract the sum of the known three numbers from the total sum of all four numbers:
[tex]\[
\text{Fourth number} = 286 - 222 = 64
\][/tex]
7. Therefore, the value of the fourth number is 64.
Hence, the correct answer is:
a. 64
