Question

Kristin and Bill are selling pies for a school fundraiser. Customers can buy apple pies and blackberry pies. Kristin sold 13 apple pies and 6 blackberry pies for a total of $354. Bill sold 11 apple pies and 2 blackberry pies for a total of $238. What is the cost of one apple pie and one blackberry pie?

Answer 1

The cost of one apple pie is $18 and the cost of one blackberry pie is $20.

Step-by-step explanation:

To find the cost of one apple pie and one blackberry pie, we need to set up a system of equations based on the information given. Let's assume the cost of one apple pie is 'a' dollars and the cost of one blackberry pie is 'b' dollars.

We have the following equations:

13a + 6b = 354 (equation 1)

11a + 2b = 238 (equation 2)

To solve this system of equations, we can use the method of substitution or elimination. Let's solve it using the method of elimination:

Multiply equation 2 by 6 to make the coefficients of 'b' in both equations the same:

66a + 12b = 1428 (equation 2)

Now subtract equation 1 from equation 2:

(66a + 12b) - (13a + 6b) = 1428 - 354

53a + 6b = 1074

Now we have a new equation:

53a + 6b = 1074 (equation 3)

Next, subtract equation 1 from equation 3:

(53a + 6b) - (13a + 6b) = 1074 - 354

40a = 720

Divide both sides by 40:

a = 18

Now substitute the value of 'a' back into one of the original equations to find the value of 'b':

11(18) + 2b = 238

198 + 2b = 238

2b = 40

Divide both sides by 2:

b = 20

Therefore, the cost of one apple pie is $18 and the cost of one blackberry pie is $20.