Question

Ja'niya earns extra money dog sitting. She charges $31.25 for 5 hours and $50 for 8 hours. How much would Ja'niya charge for 3 hours?$

Answer 1

To solve this problem we can find the linear equation that relate the hours and the price.

We know Ja'niya charges $31.25 for 5 hours and $50 for 8 hours.

We call x the hours and y the price, and we have the points (5, 31.25) and (8, 50). The equation is:

`\begin{gathered} P_1=(x_1,y_1)=(5,31.25),P_2=(x_2,y_2)=(8,50) \\ y-y_1=((y_2-y_1))/((x_2-x_1))(x-x_1) \\ y-31.25=((50-31.25))/((8-5))(x-5) \\ y=(18.75)/(3)(x-5)+31.25 \\ y=(18.75)/(3)x-5\cdot(18.75)/(3)+31.25 \\ y=(18.75)/(3)x-31.25+31.25 \\ y=(18.75)/(3)x \end{gathered}`

To find how much she charges for 3 hours we have to replace x for 3 in the equation above:

`\begin{gathered} \text{For x=3 hours:} \\ y=(18.75)/(3)\cdot3=18.75 \end{gathered}`

So, she charges $18.75 for 3 hours.