Question

How many apple pies did they sell and how many blueberry pies did they sell?

Answer 1

Let the number of apple pies x

Let the number of blue pies y

Since they sold 38 pies on Saturday, then

Add x and y, then equate the sum by 38

`x+y=38\rightarrow(1)`

Since they sold each apple pie for $11 and each blueberry pie for $13

Since they collected $460 on Saturday, then

Multiply x by 11 and y by 13, then add the products and equate the sum by 460

`11x+13y=460\rightarrow(2)`

Now, we have a system of equations to solve it

Multiply equation (1) by -13 to equate the coefficients of y in values and opposite them in signs to eliminate them

`\begin{gathered} (-13)(x)+(-13)(y)=(-13)(38) \\ -13x-13y=-494\rightarrow(3) \end{gathered}`

Add equations (2) and (3)

`\begin{gathered} (11x-13x)+(13y-13y)=(460-494) \\ -2x+0=-34 \\ -2x=-34 \end{gathered}`

Divide both sides by -2

`\begin{gathered} (-2x)/(-2)=(-34)/(-2) \\ x=17 \end{gathered}`

Substitute the value of x in equation (1) to find y

`17+y=38`

Subtract 17 from both sides

`\begin{gathered} 17-17+y=38-17 \\ y=21 \end{gathered}`

The y sold 17 apple pies and 21 blueberry pies

The answer is the last choice