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Pristine House cleaners charge $19.85 plus $32 a room. Sparkle House Cleaners charge $61.85 plus $18 a room. Write and solve an equation for which the total costs of both house cleaners is the same.



Answer :

1) Gathering the data

Pristine charges C1= $19.85 + 32r

Sparkle chargesC2= $61.85 +18r

2) The cost of both are going to be the same when a certain number of rooms is found

C1= C2

19.85 + 32r=61.85 +18r

32r-18r=61.85-19.85

14r=42

r=3

3) So the equation for which the total cost of both house cleaners is the same is:

14r -42=0

Because for r= 3

C1= $19.85 + 32r For 3 rooms

C1= $19.85 + 32(3) =$115.85

C2 =$61.85 +18r For 3 rooms

C2=$61.85 +18(3) =$115.85

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