Chapter 6, Problem 42SGR

To determine

To find the number of cakes and pies sold using elimination method.

Answer to Problem 42SGR

Pies: 18

Cakes: 22

Explanation of Solution

Given:

Total of 40 items were sold for $356.

Cost of pies is $10.

Cost of cakes is $8.

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 number of pies and y be the number of cakes.

Given that the total number of items is 40.

  $\Rightarrow x+y=40$   ......... (1)

Then 40 items were sold for $356 also, the cost of pies and cakes is $10 and $8 respectively.

  $\Rightarrow 10x+8y=356$   ......... (2)

Multiplying (1) with 10,

  $\Rightarrow 10x+10y=400$   ........... (3)

Subtracting (2) from (3),

  $\begin{array}{l}10x+10y=400\\ \frac{-10x-8y=-356}{2y=44}\end{array}$

Dividing 3 on both sides,

  $\begin{array}{c}\frac{2y}{2}=\frac{44}{2}\\ y=22\end{array}$

Substituting y in (1),

  $x+22=40$

Subtracting 22 on both sides,

  $\begin{array}{c}x+22-22=40-22\\ x=18\end{array}$

Conclusion:

The number of pies is 18 and the number of cakes is 22.