Question

a bicycle shop sells road bikes and town Cruisers. It takes 2 hours to assemble a road bike. It takes 1 hour to assemble a town Cruiser. A maximum of 60 hours a week is set aside to complete the essay for both types of bike. After assembly for safety reasons the assembly needs to be checked and tested it takes 1/2 hour to check and test the road bikes in 1/4 hour to check and test the time Cruisers a maximum of 20 hours per week is set aside to complete these tasks for both types of bike what is a system of inequalities that models the scenario select all the apply also which graph best represents the solution to the system

Answer 1

Let:

x = Number of road bikes

y = Number of town Cruisers

A maximum of 60 hours a week is set aside to complete the essay for both types of bike

so:

`2x+y\le60`

After assembly for safety reasons the assembly needs to be checked and tested it takes 1/2 hour to check and test the road bikes in 1/4 hour to check and test the time Cruisers a maximum of 20 hours per week is set aside to complete these tasks for both types of bike, so:

`(1)/(2)x+(1)/(4)x\le20`

Therefore, the system is given by:

`\begin{gathered} 2x+y\le60_{\text{ }}(1) \\ (1)/(2)x+(1)/(4)y\le20_{\text{ }}(2) \end{gathered}`
`\begin{gathered} x\ge0 \\ y\ge0 \end{gathered}`