To determine how Katie's five month average would compare to her six month average, we need to follow these steps:
1. Calculate the total tips collected over six months:
Katie's tips for each month (in dollars) are:
- June: \[tex]$133.45
- July: \$[/tex]235.31
- August: \[tex]$239.45
- September: \$[/tex]258.87
- October: \[tex]$298.45
- November: \$[/tex]115.67
The total tips collected over these six months is:
[tex]\[
133.45 + 235.31 + 239.45 + 258.87 + 298.45 + 115.67 = 1281.2
\][/tex]
2. Calculate the average tips over the six months:
To find the monthly average for the six months, divide the total tips by 6:
[tex]\[
\frac{1281.2}{6} = 213.53333333333333
\][/tex]
3. Calculate the total tips if the month of November is excluded:
Excluding November, Katie's tips for the remaining five months (in dollars) are:
- June: \[tex]$133.45
- July: \$[/tex]235.31
- August: \[tex]$239.45
- September: \$[/tex]258.87
- October: \[tex]$298.45
The total tips collected over these five months is:
\[
133.45 + 235.31 + 239.45 + 258.87 + 298.45 = 1165.53
\]
4. Calculate the average tips over the five months:
To find the monthly average for the five months, divide the total tips by 5:
\[
\frac{1165.53}{5} = 233.106
\]
5. Determine the difference in the monthly averages:
The average difference is found by subtracting the six month average from the five month average:
\[
233.106 - 213.53333333333333 = 19.572666666666663
\]
6. Conclusion:
Katie's five month average would be higher than her six month average by approximately \$[/tex]19.57.
Therefore, the correct answer is:
b. Her monthly average would have increased by \$19.57.
