Question

Two cleaning services charge money for each hour of work, plus a one-time fee.

Sparkle Team Cleaners charges according to this table:

time
(hours) cost
(dollars)
1 28
2 36
4 52
5 60
8 84


So Fresh & So Clean charges according to this graph:
1 25
2 35
3 45
4 55
5 65
6 75
7 85
8 95


1. A customer would like a company to visit their home and give a quote for their services, without doing further work. Which company is the most cost effective for this

customer? Explain your answer.

2. Another customer would like the company to perform seven hours of work. Which company should this customer choose?

3. What is the smallest number of hours of work for which Sparkle Team Cleaners is cheapest?

Answer 1

The most cost-effective company for a customer who wants a quote without further work would depend on the amount of time required for the quote. Since the prices are different for both companies, the customer should choose the one that offers the lowest price for the required amount of time. Based on the given information, we can see that Sparkle Team Cleaners charges $28 for 1 hour of work, while So Fresh & So Clean charges $25 for the same amount of time. Therefore, if the customer only needs 1 hour for the quote, Sparkle Team Cleaners would be the most cost-effective option.

To determine which company to choose for 7 hours of work, we can compare the costs of both companies at that time interval. Sparkle Team Cleaners charges $84 for 8 hours of work, while So Fresh & So Clean charges $85 for 7 hours of work. Therefore, for 7 hours of work, So Fresh & So Clean would be the better option.

To find the smallest number of hours of work for which Sparkle Team Cleaners is cheapest, we need to compare the costs of both companies at each time interval. Sparkle Team Cleaners charges $28 for 1 hour of work, $36 for 2 hours, $52 for 4 hours, $60 for 5 hours, and $84 for 8 hours. Therefore, the smallest number of hours for which Sparkle Team Cleaners is cheapest is 1 hour.

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