Question

Jana is a caterer . She's making lasagna cupcakes and Gorgonzola onion tarts for a party ,and only has a limited time to finish . She already has all her fillings ready and just needs to assemble and bake the appetizers . It takes 10 minutes to assemble each pan of lasagna cupcakes . It takes 15 minutes to roll out the Gorgonzola onion tarts and fill each pan . She has a maximum of 2 hours to assemble the appetizers . Next she needs to bake the appetizers . Each pan of lasagna cupcakes takes 20 minutes to bake . Each pan of Gorgonzola tarts takes 6 minutes to bake . She has 60 minutes to bake the appetizers . What system of inequalities that models this scenario ? CHECK ALL THAT APPLY . Also how would those inequalities look graphed ?

Answer 1

Answer::

`\begin{gathered} 20x+6y\le60 \\ 10x+15y\le120 \\ x\ge0 \\ y\ge0 \end{gathered}`

Step-by-step explanation:

Let the number of lasagna cupcakes made = x

Let the number of Gorgonzola onion tarts made = y

0. It takes ,10 minutes, to assemble each pan of lasagna cupcakes.

,

1. It takes ,15 minutes, to roll out the Gorgonzola onion tarts and fill each pan.

,

2. She has a maximum of ,2 hours (120 minutes), to assemble the appetizers.

These translate to the inequality:

`10x+15y\le120`

0. Each pan of lasagna cupcakes takes 20 minutes to bake.

,

1. Each pan of Gorgonzola tarts takes 6 minutes to bake.

,

2. She has 60 minutes to bake the appetizers.

These translate to the inequality:

`20x+6y\le60`

Since she must bake either lasagna cupcakes or Gorgonzola tarts, we have that:

`\begin{gathered} x\ge0 \\ y\ge0 \end{gathered}`

So the system of inequalities is:

`\begin{gathered} 20x+6y\le60 \\ 10x+15y\le120 \\ x\ge0 \\ y\ge0 \end{gathered}`

The graph that bests represents this scenario is: