when babysitting, emily charges $5.50 per hour before midnight,and $4.50 after midnight.she earned $28.75 for taking care of the Bradford triplets until 1:30 in the morning. What time did Emily begin her babysitting job?
plzzzzzzz help me! i've wasted 2 hours trying to figure out this problem and keep ending up with like "500" different answers!
4.5 * 1.5 = 6.75 after midnight
28.75 - 6.75 = 22
22/5.5 = 4
12:00 - 4 = 8:00
8 O'Clock. (Only 5 years late!) :)
Sure, I'd be happy to help you solve this problem and explain the steps along the way. Let's break it down.
Step 1: Determine the number of hours worked before midnight and after midnight.
- Let's assume Emily worked x hours before midnight and y hours after midnight.
Step 2: Write an equation based on the information given.
- Emily charges $5.50 per hour before midnight, so the amount she earned for this time period is 5.50 * x.
- Emily charges $4.50 per hour after midnight, so the amount she earned for this time period is 4.50 * y.
- The total amount she earned is $28.75, so we can set up the equation: 5.50x + 4.50y = 28.75.
Step 3: Use the given time to create a second equation.
- Emily worked until 1:30 in the morning, which is 1 hour and 30 minutes after midnight.
- Since 1 hour is before midnight and 30 minutes is after midnight, we can set up the equation: x + 0.5y = 1.5.
Step 4: Solve the system of equations.
- We now have a system of linear equations:
5.50x + 4.50y = 28.75
x + 0.5y = 1.5
- We can solve this system using substitution or elimination. Let's use the substitution method in this case.
- Solve the second equation for x: x = 1.5 - 0.5y.
- Substitute this value of x in the first equation: 5.50(1.5 - 0.5y) + 4.50y = 28.75.
- Simplify and solve for y: 8.25 - 2.75y + 4.50y = 28.75.
-2.75y + 4.50y = 28.75 - 8.25
1.75y = 20.50
y = 20.50 / 1.75
y ≈ 11.7143
Step 5: Find x using the value of y.
- Substitute the value of y back into the second equation: x + 0.5(11.7143) = 1.5.
- Simplify and solve for x: x ≈ -5.857.
Step 6: Interpret the answer.
- Since it doesn't make sense for the number of hours before midnight to be negative, we can discard the negative value of x.
- This means that Emily worked approximately 11.7143 hours after midnight, which translates to 11 hours and 43 minutes.
- Therefore, Emily began her babysitting job 11 hours and 43 minutes before 1:30 in the morning.
- Subtracting 11 hours and 43 minutes from 1:30 in the morning gives us the starting time: 1:30 - 11 hours 43 minutes ≈ 1:30 PM the previous day.
So, Emily began her babysitting job at approximately 1:30 PM the previous day.