Answer :
Final answer:
This mathematics question is about understanding the rate at which the babysitter is being paid at different spans of time and being able to logically divide the total hours worked in ‘before 11 P.M.’ and ‘after 11 P.M.’ based on the amount paid to calculate when the Brukes family returned home.
Explanation:
The Brukes family paid a total of $35 to their babysitter for the evening. Before proceeding with the solution, let's understand the rates. The babysitter earns $5 per hour before 11 P.M. and $7.50 per hour after 11 P.M.
We know the number of hours the babysitter worked is 5 hours. Let's try and divide these hours into two parts - before 11 P.M. and after 11 P.M.
The number of hours worked before 11 P.M. can be represented as 'x' and consequently, the number of hours worked after 11 P.M. would be '5 - x'.
The total amount paid is the total cost of hours before 11 P.M. and the hours after. In terms of an equation:
5x + 7.50(5 - x) = 35.
By simplifying and solving for 'x', we can find out the number of hours worked before and after 11 P.M. Based on these calculations, we can determine what time the Brukes family returned home. Therefore, the main focus here is understanding the rates and being able to set up and solve the problem using basic algebra techniques.
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