Question

A chocolate factory has a goal to produce10121012pounds of chocolate frogs per day. If the machines operate for712712hours per day making215215pounds of chocolate frogs per hour, will the chocolate factory make it’s goal?The chocolate factory meet their goal with the total being10121012pounds of chocolate frogs produced.

Answer 1

First, rewrite all the mixed fractions as impropper fractions:

`\begin{gathered} 10(1)/(2)=10*(2)/(2)+(1)/(2)=(20)/(2)+(1)/(2)=(21)/(2) \\ \\ 7(1)/(2)=7*(2)/(2)+(1)/(2)=(14)/(2)+(1)/(2)=(15)/(2) \\ \\ 2(1)/(5)=2*(5)/(5)+(1)/(5)=(10)/(5)+(1)/(5)=(11)/(5) \end{gathered}`

Next, multiply the rate of chocolate production over time by the the operating time of the machines to find the total amount of pounds of chocolate frogs produced in one day:

`7(1)/(2)*2(1)/(5)=(15)/(2)*(11)/(5)=(15*11)/(2*5)=(3*11)/(2)=(33)/(2)=16(1)/(2)`

Then, the chocolate factory can produce 16 1/2 pounds of chocolate frogs per day.

Since 16 1/2 is greater than 10 1/2, then the chocolate factory will meet their goal with the total being over 10 1/2 pounds of chocolate frogs produced.