Final answer:
Using a system of linear equations based on Mofor's and Kathryn's pie sales, the cost of one blueberry pie was found to be $13, and the cost of one pumpkin pie was found to be $14.
Step-by-step explanation:
To solve for the cost of one blueberry pie and one pumpkin pie, we can use a system of linear equations, which is derived from the information given about the sales by Mofor and Kathryn. Mofor's sales can be represented as the first equation, 2B + 7P = 124, where B is the cost of a blueberry pie and P is the cost of a pumpkin pie. Kathryn's sales can be represented as the second equation, 7B + 7P = 189.
First, we solve the system of equations. To simplify, we can divide Kathryn's equation by 7, which gives B + P = 27. Now we subtract Mofor's equation from this simplified equation to eliminate P and solve for B.
By subtracting 2B + 7P from B + P, we are left with -B = 27 - 124, which simplifies to B = 97. Dividing by -1, we find B, the cost of a blueberry pie is 97 dollars. Now that we have the cost of a blueberry pie, we can substitute this value back into any of our original equations to find P, the cost of a pumpkin pie. Using Mofor's equation: 2(97) + 7P = 124, P is calculated as follows: 194 + 7P = 124, subtracting 194 from both sides, we get 7P = -70, then divide by 7 to get P = -10.
However, since a pie cannot have a negative cost, let's re-evaluate our calculations. After dividing Kathryn's equation by 7, we get B + P = 27. Now let's multiply Mofor's equation by -1 to make elimination easier when we subtract it from Kathryn's simplified equation: -2B - 7P = -124. Adding this to Kathryn's equation, 7B + 7P = 189, leads to 5B = 65, which after dividing by 5 yields B = 13.
Substituting B = 13 into either equation to solve for P, let's use Mofor's equation again: 2(13) + 7P = 124. This leads to 26 + 7P = 124, subtracting 26 from both sides gives us 7P = 98. Dividing by 7 gives us P = 14.
Therefore, the cost of one blueberry pie is $13, and the cost of one pumpkin pie is $14.