Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Yesterday a chef used 32 eggs to make 2 chocolate souffles and 6 lemon meringue pies. The day before, he made 2 chocolate souffles and 10 lemon meringue pies, which used 48 eggs. How many eggs does each dessert require? A chocolate souffle requires __ eggs and a lemon meringue pie requires __ eggs.

Answer 1

`\begin{gathered} 2x+6y=32 \\ 2x+10y=48 \end{gathered}`

the system of equations above represent the question, we need to solve the system in order to know the number of eggs necessary for each dessert

x is the number of eggs used to make the chocolate souffle.

y is the number of eggs used to make lemon meringue pies.

First, we need to multiply the second equation with -1 so we have

`-2x-10y=-48`

we will sum the first equation with the equation above

`\begin{gathered} -4y=-16 \\ y=(-16)/(-4)=4 \\ y=4 \end{gathered}`

we substitute the value of y in the first equation

`\begin{gathered} 2x+6(4)=32 \\ 2x+24=32 \\ 2x=32-24 \\ 2x=8 \\ x=(8)/(2) \\ x=4 \end{gathered}`

A chocolate souffle requires 4 eggs and a lemon meringue pie requires 4 eggs.​