Question

At the school cafeteria, the cost of one milk is $.50. The total cost of 5 turkey sandwiches and 4 milks is the same as the total cost of 4 turkey sandwiches and 8 milks. Write an equation that can be used to find the cost of a turkey sandwich. Explain what each expression or value represents in the equation. b. Use the equation you wrote in part a. to find the cost of a turkey sandwich. Explain how you solved the equation.

Answer 1

The total cost of one milk is $0.50,

Let 'y' represents the cost of one milk,

Let 'x' represents the cost of turkey sandwiches,

5 turkey sandwiches will be 5 × x= 5x

4 milks will be 4 × y= 4y

4 turkey sandwiches will be 4 × x = 4x

8 milks will be 8 × y = 8y

Let us now get the equation to solve for the cost of turkey sandwich,

`\begin{gathered} 5x+4y=4x+8y \\ \text{collect like terms,} \\ 5x-4x=8y-4y \\ x=4y \\ \text{Therefore, the equation used to solve for the cost of a turkey sandwich} \\ is, \\ x=4y \\ \text{where x is the cost of one turkey sandwich} \\ y\text{ is the cost one of one milk} \end{gathered}`

Hence, the equation is x = 4y.

Let us now solve for the cost of a turkey sandwich,

`\begin{gathered} \text{Given,} \\ x=4y \\ \text{where y= \$0.50} \end{gathered}`
`\begin{gathered} x=4*\text{ \$0.50} \\ x=\text{ \$2} \end{gathered}`

Hence, the cost of a turkey sandwich is $2.