Question

a group of high school students volunteered to help a local organization on repairs to an old home in the community. the school receives total time credit for supporting the local organization. the school transports the students by bus to the event. the students arrive at the site at 11:00 am and leave to return to school at 4:30 pm. the teacher sponsor for this event has already spent 120 minutes on site preparing for the day. if a total of 41 students and chaperones participated on the day of the event, how many total hours did the school have someone on site at the local home? write an equation and solve to find the answer
$y = 5x + 2$
$y = 5×41 + 2$
$y = 184.5 + 2$
$y = 182.5$ hours
$y = 5.5x + 2$
$y = 5.5×41 + 2$
$y = 225.5 + 2$
$y = 227.5$ hours
$y = 5.5x + 1.2$
$y = 5.5×41 + 1.2$
$y = 225.5 + 1.2$
$y = 226.7$ hours
$y = 5.5x - 2$
$y = 5.5×41 - 2$
$y = 225.5 - 2$
$y = 223.5$ hours

Explanation:

Step1: Determine time students/chaperones spent

Students arrive at 11:00 AM and leave at 4:30 PM. Time duration: 5.5 hours (since 16:30 - 11:00 = 5.5 hours). Let \( x \) be number of people (41 students + chaperones? Wait, total people \( x = 41 \)? Wait, the teacher spent 120 minutes (2 hours) preparing. Wait, the equation should model total time: time per person (5.5 hours) times number of people (41) plus teacher's prep time (2 hours, since 120 minutes = 2 hours). So the correct equation starts with \( y = 5.5x + 2 \), where \( x = 41 \).

Step2: Substitute \( x = 41 \) into the equation

\( y = 5.5 \times 41 + 2 \)

Step3: Calculate \( 5.5 \times 41 \)

\( 5.5 \times 41 = 225.5 \)

Step4: Add 2 to the result

\( y = 225.5 + 2 = 227.5 \)

Answer:

The correct equation and solution is \( y = 5.5x + 2 \), \( y = 5.5 \times 41 + 2 \), \( y = 225.5 + 2 \), \( y = 227.5 \) hours. So the correct option is the one with \( y = 5.5x + 2 \), \( y = 5.5 \times 41 + 2 \), \( y = 225.5 + 2 \), \( y = 227.5 \) hours (the second option group).