Question

The cost (c) to hire a dog trainer is varies directly with the amount of time (h) in hours spent training the dog.

Part A

Write an equation to represent the proportional relationship between c and h using the information given. c =

Part B Sue spent $660 on 12 hours of obedience training for her dog Muffin. Jon wants to use the same dog trainer for his dog Tex, but he only has $440 to spend. How many hours of training can he get for Tex? Explain your reasoning.

Answer 1

Part A) The proportional equation is
`c=55h`

Part B) 8 hours of training

Explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`y/x=k` or
`y=kx`

Let

c -----> the cost to hire a dog

h ----> the amount of time in hours

The linear equation is equal to

`c=kh`

Sue spent $660 on 12 hours of obedience training for her dog Muffin

Find the value of k (constant of proportionality)

`k=y/x`

substitute the values

`k=660/12=55`

therefore

The linear equation is

`c=55h`

For
`c=\$440`

Find the value of h

substitute in the equation and solve for h

`440=55h`

`h=440/55=8\ hours`