Question

Castel and Julio are selling pies for a school fundraiser. Customers can buy apple pies and pumpkin pies. Castel sold 9 apple pies and 3 pumpkin pies for a total of $54. Julio sold 11 apple pies and 3 pumpkin pies for a total of $62. Find the cost each of one apple pie and one pumpkin pie.

Answer 1

let's call the apple pies "x" and "y" the pumpkin pies

now we are going to put 9x + 3y = 54 which is what Castel sold

and below this we are going to put 11x + 3y = 62 which is what Julio sold.

After this we choose one of the methods to solve these types of equations, in this case I will choose the equalization method so we do the following:

Explanation:

in this case I am going to clear the "y" because is easier

1st step:

9x + 3y = 54 3y = 54 - 9x y = (54-9x)/3

-> ->

11x + 3y = 62 3y = 62 - 11x y = (62-11x)/3

2nd step:

we remove that 3 that is dividing the entire ecuation and it would be like this:

54-9x=62-11x

we put the "x" to one side and the other numbers to the other

-9x+11x=62-54

and we solve it

2x=8 -> x=8/2 -> x=4

3rd step:

We already know what the "x" is, now we need to know the "y" for doing this we take one of the first ecuations, i'm going to take this:

3y = 54 - 9x

We substitute the "x" for the number that has come out, in this case the 4

3y = 54 - 9 · 4

and we solve it

3y = 54 - 9 · 4

3y = 54 - 36

3y = 18

y = 18/3

y = 6

and our results are

x = 4

y = 6

so apple pies that were "x" would cost 4$ and pumpkin pies that were "y" would cost 6$