Question

The amount of shampoo that a pet groomer uses per day is proportional to the number of dogs groomed. The pet groomer uses 26.25 ounces of shampoo per day when 7 dogs need to be groomed.

Write an equation to represent this relationship. Express the constant of proportionality as a decimal.

Answer 1

`\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill`

`\stackrel{\textit{`

Answer 2

This equation shows that the pet groomer uses 3.75 ounces of shampoo per dog.

The relationship between the amount of shampoo used and the number of dogs groomed is proportional. We can represent this relationship with an equation using the form y = kx, where y is the amount of shampoo used, x is the number of dogs groomed, and k is the constant of proportionality.

Given that the pet groomer uses 26.25 ounces of shampoo per day when 7 dogs need to be groomed, we can use this information to find the value of k.

26.25 = k * 7

Solving for k, we get:

k = 26.25/7

k = 3.75

So the equation representing the relationship between the amount of shampoo used and the number of dogs groomed is y = 3.75x

This equation shows that the pet groomer uses 3.75 ounces of shampoo per dog.