Question

Eugene and Dan'are are participating in a school fundraiser by selling cherry pies and pumpkin pies. Eugene sold 2 cherry pies and 10 pumpkin pies, resulting in total sales of $214. Dan sold 5 cherry pies and 5 pumpkin pies, with total sales of $155. What is the cost of one cherry pie and one pumpkin pie?

Answer 1

Using a system of equations, the cost of one cherry pie was determined to be $12, and the cost of one pumpkin pie was found to be $19.

Step-by-step explanation:

The question asks us to find the cost of one cherry pie and one pumpkin pie using a system of equations approach. We are given two scenarios where Eugene sold 2 cherry pies and 10 pumpkin pies for a total of $214, and Dan sold 5 cherry pies and 5 pumpkin pies for a total of $155.

To find the individual prices, we set up two equations based on the information provided:

• 2C + 10P = 214 (Eugene's sales)
• 5C + 5P = 155 (Dan's sales)

We can solve this system of equations using either substitution or elimination method to find the values of C (the cost of one cherry pie) and P (the cost of one pumpkin pie).

Let's use the elimination method as an example:

1. Multiply the second equation by 2 to line up the coefficients for C: 10C + 10P = 310.
2. Subtract the first equation from this new equation: (10C + 10P) - (2C + 10P) = 310 - 214.
3. This simplifies to 8C = 96, and dividing both sides by 8 gives us C = 12.
4. Now, substitute C = 12 into one of the original equations to find P. Using Eugene's equation: 2(12) + 10P = 214, which simplifies to 24 + 10P = 214. Subtract 24 from both sides: 10P = 190, and divide by 10 to get P = 19.

Therefore, the cost of one cherry pie is $12 and the cost of one pumpkin pie is $19.