Question

A breakfast menu lists 2 eggs with 1 sausage patty for $2.23 and 3 eggs with 2 sausage patties for $3.76. How much do you pay for each egg and how much for each sausage patty? How much would you expect to pay for the Glutton's Breakfast of 5 eggs and 7 sausage patties?

Answer 1

• The cost per egg is $0.7, and the cost per sausage patty is $0.83.

,

• You would expect to pay $9.31 for Glutton's Breakfast.

Step-by-step explanation:

• Let the cost per egg = e

,

• Let the cost per sausage patty = p

2 eggs with 1 sausage patty cost $2.23

`2e+p=2.23\ldots(1)`

3 eggs with 2 sausage patties cost $3.76

`3e+2p=3.76\ldots(2)`

We solve the system of linear equations for e and p.

From the first equation:

`p=2.23-2e`

Substitute into equation (2):

`\begin{gathered} 3e+2p=3.76 \\ 3e+2(2.23-2e)=3.76 \\ 3e+4.46-4e=3.76 \\ -e+4.46=3.76 \\ e=4.46-3.76 \\ e=0.7 \end{gathered}`

Next, solve for p:

`\begin{gathered} p=2.23-2e \\ =2.23-2(0.7) \\ p=0.83 \end{gathered}`

The cost per egg, e is $0.7, and the cost per sausage patty, p is $0.83.

Next, we find out how much you would expect to pay for Glutton's Breakfast.

`\begin{gathered} 5e+7p=5(0.7)+7(0.83) \\ =3.5+5.81 \\ =9.31 \end{gathered}`

You would expect to pay $9.31 for Glutton's Breakfast.