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41 votes
41 votes
Richard has two different plans for his business. Plan 1: He charges $3 per hour to walk a dog plus $10 for grooming at the end of the walk. Plan 2: He charges $5 per hour to walk a dog and then offers free grooming at the end of the walk. Part A Write an equation to model the time in hours, h, when the two plans cost the same amount. Part B When will the two plans in hours, h, cost the same amount? h =

User GoGoris
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1 Answer

13 votes
13 votes

First, write an equation for the amount of money he wins for each plan, given a time of h hours:


\begin{gathered} P_1=10+3h \\ P_2=5h \end{gathered}

If both plans cost the same amount, then P_1 = P_2, therefore:


10+3h=5h

Solve the equation for h:


\begin{gathered} \Rightarrow10=5h-3h\text{ } \\ =2h \\ \Rightarrow h=(10)/(2) \\ \Rightarrow h=5 \end{gathered}

Therefore, for Part A the equation is 10+3h=5h

For Part B, the value of h when both plans cost the same amount is h=5.

User Beatriz
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