For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response.

Question

A company sells hats, and the business can be represented by the piecewise function and graph below. The y-values represent the total cost of the purchase, and the x-values represent the number of hats purchased.

y={12x if 0≤x≤10 8.5x if x > 10}

Part A: Determine the total cost of purchasing 8 hats. Show all work.

Part B: If 75 hats are purchased, what is the total cost? Show all work.

Part C: In your own words, explain the total cost of hat purchases for this company.

Answer 1

Hi Ria,

A company sells hats, and the business can be represented by the piecewise function and graph below. The y-values represent the total cost of the purchase,

and the x-values represent the number of hats purchased.

y={12x if 0≤x≤10 8.5x if x > 10}

This is a piecewise function

y={12x if 0≤x≤10 8.5x if x > 10}

y = 12x if 0 ≤ x ≤ 10

This means that when x greater than or equal to 0 and less than or equal to 10,

y =12x

y = 8.5x if x > 10

This means that if x is greater than 10

y = 8.5 x

Part A: Determine the total cost of purchasing 8 hats. Show all work.

Given 8 hats find total cost

8 falls between 0 and 10.. Therefor we use the 1st equation

y = 12x if 0 ≤ x ≤ 10

y=12(8) = 96

Part B: If 75 hats are purchased, what is the total cost? Show all work.

75 is greater than 10 so use the 2nd equation

y = 8.5x if x > 10

y=8.5(75)=637.5

Part C: In your own words, explain the total cost of hat purchases for this company.

I'll leave you to explain in your own words.. Note: the total costs changes once you have sold more than 10 hats.

Hope this helps!

Let me know if you have any more questions.