Answer :
To find the fourth number when the mean of four numbers is 71.5 and three of those numbers are 58, 76, and 88, we can follow these steps:
1. Understand the mean formula: The mean (average) of a set of numbers is calculated by adding all the numbers together and then dividing by the total number of numbers. Here, the mean of four numbers is given as 71.5.
2. Set up the equation:
- Let's call the fourth number [tex]\( x \)[/tex].
- We know the mean of the four numbers is 71.5, so:
[tex]\[
\frac{58 + 76 + 88 + x}{4} = 71.5
\][/tex]
3. Calculate the total sum of the four numbers:
- Multiply the mean by the number of numbers to find the total sum:
[tex]\[
71.5 \times 4 = 286
\][/tex]
- Therefore, the sum of all four numbers is 286.
4. Find the sum of the known numbers:
- Add the three known numbers together:
[tex]\[
58 + 76 + 88 = 222
\][/tex]
5. Calculate the fourth number:
- Subtract the sum of the known numbers from the total sum to find the fourth number:
[tex]\[
286 - 222 = 64
\][/tex]
So, the fourth number is [tex]\( \boxed{64} \)[/tex].
1. Understand the mean formula: The mean (average) of a set of numbers is calculated by adding all the numbers together and then dividing by the total number of numbers. Here, the mean of four numbers is given as 71.5.
2. Set up the equation:
- Let's call the fourth number [tex]\( x \)[/tex].
- We know the mean of the four numbers is 71.5, so:
[tex]\[
\frac{58 + 76 + 88 + x}{4} = 71.5
\][/tex]
3. Calculate the total sum of the four numbers:
- Multiply the mean by the number of numbers to find the total sum:
[tex]\[
71.5 \times 4 = 286
\][/tex]
- Therefore, the sum of all four numbers is 286.
4. Find the sum of the known numbers:
- Add the three known numbers together:
[tex]\[
58 + 76 + 88 = 222
\][/tex]
5. Calculate the fourth number:
- Subtract the sum of the known numbers from the total sum to find the fourth number:
[tex]\[
286 - 222 = 64
\][/tex]
So, the fourth number is [tex]\( \boxed{64} \)[/tex].
