10. On a certain hot summer day 481 people used the public swimming pool The daily prices are 1.25 for children and 2.25 for adults. The receipts for admission totaled 865.25 .How many children and how many adults swam at the public pool that day?

Let's denote the number of children as $x$ and the number of adults as $y$. We can set up a system of linear equations based on the given information:<br /><br />1. The total number of people is 481:<br />\[ x + y = 481 \]<br /><br />2. The total amount of money collected is $865.25:<br />\[ 1.25x + 2.25y = 865.25 \]<br /><br />Now, let's solve this system of equations step by step.<br /><br />First, solve the first equation for $x$:<br />\[ x = 481 - y \]<br /><br />Next, substitute this expression for $x$ into the second equation:<br />\[ 1.25(481 - y) + 2.25y = 865.25 \]<br /><br />Simplify and solve for $y$:<br />\[ 1.25 \cdot 481 - 1.25y + 2.25y = 865.25 \]<br />\[ 600.25 - 1.25y + 2.25y = 865.25 \]<br />\[ 600.25 + 1y = 865.25 \]<br />\[ 1y = 865.25 - 600.25 \]<br />\[ y = 265 \]<br /><br />So, there were 265 adults.<br /><br />Now, substitute $y = 265$ back into the first equation to find $x$:<br />\[ x + 265 = 481 \]<br />\[ x = 481 - 265 \]<br />\[ x = 216 \]<br /><br />Therefore, there were 216 children and 265 adults who swam at the public pool that day.