Question
Logan has the following data:
r81115811
If the mean is 10, which number could r be?
r81115811
If the mean is 10, which number could r be?
Answers
GPT-4o mini
To find the value of \( r \) in the number \( r81115811 \) such that the mean of all digits is 10, we first need to calculate the total number of digits and the desired total sum of those digits.
The number consists of 9 digits: \( r, 8, 1, 1, 1, 5, 8, 1, 1 \).
1. **Calculate the sum of the known digits:**
\[
8 + 1 + 1 + 1 + 5 + 8 + 1 + 1 = 26
\]
2. **Let \( S \) be the total sum of the digits, which includes \( r \):**
\[
S = r + 26
\]
3. **Calculate the mean:**
The mean of all digits is given by:
\[
\text{Mean} = \frac{S}{\text{Number of digits}} = \frac{r + 26}{9}
\]
According to the problem, this mean equals 10:
\[
\frac{r + 26}{9} = 10
\]
4. **Multiply both sides by 9 to eliminate the fraction:**
\[
r + 26 = 90
\]
5. **Solve for \( r \):**
\[
r = 90 - 26 = 64
\]
Thus, the value of \( r \) that satisfies the condition is \( r = 64 \).
Since \( r \) needs to be a single digit, it appears that no single digit value can make the mean 10 under these constraints (where \( r \) must be a digit from 0-9). Therefore, it's likely the condition provided cannot be satisfied with a valid single-digit \( r \).
In conclusion, the equation results in \( r = 64 \), which is not valid since \( r \) must be a digit (0-9). Thus, there are no digits \( r \) that can satisfy the given mean of 10 with the specified digits.
The number consists of 9 digits: \( r, 8, 1, 1, 1, 5, 8, 1, 1 \).
1. **Calculate the sum of the known digits:**
\[
8 + 1 + 1 + 1 + 5 + 8 + 1 + 1 = 26
\]
2. **Let \( S \) be the total sum of the digits, which includes \( r \):**
\[
S = r + 26
\]
3. **Calculate the mean:**
The mean of all digits is given by:
\[
\text{Mean} = \frac{S}{\text{Number of digits}} = \frac{r + 26}{9}
\]
According to the problem, this mean equals 10:
\[
\frac{r + 26}{9} = 10
\]
4. **Multiply both sides by 9 to eliminate the fraction:**
\[
r + 26 = 90
\]
5. **Solve for \( r \):**
\[
r = 90 - 26 = 64
\]
Thus, the value of \( r \) that satisfies the condition is \( r = 64 \).
Since \( r \) needs to be a single digit, it appears that no single digit value can make the mean 10 under these constraints (where \( r \) must be a digit from 0-9). Therefore, it's likely the condition provided cannot be satisfied with a valid single-digit \( r \).
In conclusion, the equation results in \( r = 64 \), which is not valid since \( r \) must be a digit (0-9). Thus, there are no digits \( r \) that can satisfy the given mean of 10 with the specified digits.