Question

Part A This question has four parts. A bakery owner has two doughnut glazing machinesThe first machine can glaze 25 dozen doughnuts per hour. Based on this rate what is the total number of dozens of doughnuts the first machine can glaze in 6 hours? Show or explain how you got your answer. Enter your answer and your work or explanation in the space provided Part B The second doughnut-glazing machine can glaze 75 dozen doughnuts in 2 hours Based on this ratewhat is the total number of hours it will take the second machine to glaze 135 dozen doughnuts ? Show or explain how you got your answer Part C The bakery owner will use both machines to glaze a total of 375 dozen doughnuts She plans to start both machines at the same time Based on the rates from Parts A and B what is the number of hours it will take both machines working together to glaze 375 dozen doughnuts? Show or explain how you got your answer. Part D What percent of the 375 dozen doughnuts in Part C were glazed by the first machine ? Show or explain how you got your answer

Answer 1

A) Using the rate 25 dozen doughnuts per hour, we get:

`6\text{ hours}\cdot\frac{25\text{ dozen}}{1\text{ hour}}=6\cdot25\text{ dozen =}150\text{ dozen of doughnuts}`

B) ) Using the rate 75 dozen doughnuts in 2 hours, we get:

`135\text{ dozen}\cdot\frac{2\text{ hours}}{75\text{ dozen}}=(135\cdot2)/(75)hours=3.6\text{ hours}`

C) Let's call x to the number of hours that both machines take to glaze 375 dozen of doughnuts. Similarly than Part A, we need to multiply the number of hours that a machine work by its rate to get the total number of dozen of doughnuts glazed. That is,

`\begin{gathered} (25)/(1)x+(75)/(2)x=375 \\ (50+75)/(2)x=375 \\ (125)/(2)x=375 \\ x=375\cdot(2)/(125) \\ x=6\text{ hours} \end{gathered}`

D) In 6 hours, the first machine glaze 150 dozen of doughnuts (see part A).

If 375 dozen represents 100%, then we can use the next proportion to find what perentage represents 150 dozen.

`\frac{375\text{ dozen}}{150\text{ dozen}}=\frac{100\text{ \%}}{x\text{ \%}}`

Solving for x,

`\begin{gathered} 375\cdot x=100\cdot150 \\ x=(15000)/(375) \\ x=40\text{ \%} \end{gathered}`