Chapter 6, Problem 52SGR

To determine

To calculate the cost of one slice of pizza and an order of French fries.

Answer to Problem 52SGR

Cost of one slice of pizza: $3.75

Cost of one order of French fries: $3.00

Explanation of Solution

Given:

The cost of 4 slices of pizza and 2 orders of French fries is $21.00

The cost of 2 slices of pizza and 3 orders of French fries is $16.50

Concept used:

Assume separate variables for each object. Form two equations with the variables. Use elimination method and solve the system of equations.

Calculation:

Let x be the cost of one slice of pizza and y be the cost of one order of French fries.

Since the cost of 4 slices of pizza and 2 orders of French fries is $21.00

  $\Rightarrow 4x+2y=21.00$ ……… (1)

The cost of 2 slices of pizza and 3 orders of French fries is $16.50

  $\Rightarrow 2x+3y=16.50$ ………. (2)

Multiplying (2) with 2,

  $\Rightarrow 4x+6y=33.00$ ……… (3)

Subtracting (1) from (3),

  $\begin{array}{l}4x+6y=33.00\\ \frac{-4x-2y=-21.00}{4y=12.00}\end{array}$

Dividing 4 on both sides,

  $\begin{array}{c}\frac{4y}{4}=\frac{12.00}{4}\\ y=3.00\end{array}$

Substituting y in (1)

  $\begin{array}{c}4x+2(3.00)=21.00\\ 4x+6.00=21.00\end{array}$

Subtracting 6.00 on both sides,

  $\begin{array}{l}4x+6.00=21.00-6.00\\ 4x=15.00\end{array}$

Dividing 4 on both sides

  $\begin{array}{c}\frac{4x}{4}=\frac{15.00}{4}\\ x=3.75\end{array}$

Conclusion:

The cost of one slice of pizza is $3.75 and the cost of one order of French fries is $3.00