Question

On the first day, a total of 40 items were sold for$\mathbf{\backslash (}\mathbf{356}$. Define the variables, and write equations to find the number of cakes and pies sold. Solve by using elimination.

Monarch Middle School
Bake sale
Pies	$\mathbf{\backslash )}\mathbf{10}$
Cakes	$\mathbf{\$}\mathbf{8}$

Short answer

The number of cakes and pies sold are 22 and 18 respectively.

Step-by-step solution

Step 1. State the concept of elimination method.

The elimination method is the method in which addition or subtraction method is used to get an equation in the one variable.

If the coefficients are opposite, use the addition and when the coefficients are same, use the subtraction.

Step 2. Add or subtract the equations to eliminate one variable.

Let the number of cakes be$x$and the number of pies be$y$.

As per the conditions the system of equations thus formed will be:

$x+y=40$ … (1)

$8x+10y=356$ … (2)

Multiply equation (1) by 8.

$\begin{array}{c}8(x+y)=8\times \left(40\right)\\ 8x+8y=320\left(3\right)\end{array}$

Note that both the equations (2) and (3) havelocalid="1647579462957" $8x$in same sign, therefore, variablelocalid="1647579475744" $x$can be eliminated if both equations are subtracted.

$\begin{array}{l}8x+8y=320\\ \underset{¯}{(-)8x+10y=356}\\ -2y=-36\text{Dividebothsidesby-2}\\ y=18\end{array}$

Step 3. Solve for x. 

Substitute 18 for$y$into the equation (1) and solve for$x$.

$\begin{array}{c}x+y=40\\ x+\left(18\right)-18=40-18\\ x=22\end{array}$

Therefore, the number of cakes and pies sold are 22 and 18 respectively.