the amount lucy earned babysitting each month for the past five months was $225, $280, $240, $180, and $200…

Explanation:

Step1: Recall the mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $\bar{x}$ is the mean, $n$ is the number of data - points, and $\sum_{i = 1}^{n}x_{i}$ is the sum of the data - points. We know $n = 6$ and $\bar{x}=220$, so the sum of the six - month earnings $\sum_{i = 1}^{6}x_{i}=n\times\bar{x}=6\times220 = 1320$.

Step2: Calculate the sum of the first five - month earnings

The sum of the first five - month earnings is $225 + 280+240 + 180+200=1125$.

Step3: Find the sixth - month earnings

Let the sixth - month earnings be $x$. Then $\sum_{i = 1}^{6}x_{i}=(225 + 280+240 + 180+200)+x$. We know $\sum_{i = 1}^{6}x_{i}=1320$ and the sum of the first five is $1125$. So $1320=1125 + x$. Solving for $x$, we get $x=1320 - 1125=195$.

Answer:

195