Question

The relationship between the number of hours a plumber works and the total work fee she charges is proportional. Her fee for 555 hours of work is $350. Which of the following could be combinations of values for the plumber's work hours and total work fee she charges? Choose 3 answers:

a) 333 hours and $270

b) 3.5 hours and $245

c) 666 hours and $420

d) 7.25 hours and $507.50

e) 888 hours and $490

Answer 1

By finding the hourly rate of the plumber ($0.63 per hour), it's determined that the possible correct combinations of work hours and total fees charged under the proportional relationship are only option c) 666 hours and $420.

Step-by-step explanation:

The relationship between the number of hours a plumber works and the total work fee charged is proportional. We know that the plumber's fee for 555 hours is $350. To find out the hourly rate, we divide the total fee by the number of hours: $350 ÷ 555 hours = $0.63 per hour. Using this hourly rate, we can calculate the total fees for different hours of work to determine which options are correct.

The formula to calculate the total work fee is Total fee = hourly rate × number of hours worked.

1. 333 hours × $0.63/hour = $209.79, so option a) 333 hours and $270 is incorrect.
2. 3.5 hours × $0.63/hour = $2.205, so option b) 3.5 hours and $245 is incorrect.
3. 666 hours × $0.63/hour = $419.58, so option c) 666 hours and $420 is correct.
4. 7.25 hours × $0.63/hour = $4.5675, so option d) 7.25 hours and $507.50 is incorrect.
5. 888 hours × $0.63/hour = $559.44, so option e) 888 hours and $490 is incorrect.

Therefore, the combinations of hours and total fees that could be correct for the plumber's proportional fee structure are option c) 666 hours and $420.