Final answer:
The cost of one pecan cheesecake is $14, and the cost of one apple cheesecake is $15. This was calculated using a system of linear equations representing the sales made by Daniel and Dan, manipulating the equations to isolate and find the values of 'p' and 'a,' which are the prices per pecan and apple cheesecake, respectively.
Step-by-step explanation:
To find the cost of one pecan cheesecake and one apple cheesecake, we can set up a system of linear equations to represent the sales made by Daniel and Dan.
Let p be the price of one pecan cheesecake and a be the price of one apple cheesecake. We can set up the following equations based on the information provided:
- Daniel sold: 12p + 5a = $243
- Dan sold: 14p + 13a = $391
Multiplying the first equation by 14 and the second equation by 12 gives us a new set of equations:
- 14(12p + 5a) = 14 * $243
- 12(14p + 13a) = 12 * $391
After simplifying, we have:
- 168p + 70a = $3402
- 168p + 156a = $4692
Subtracting the fourth equation from the third, we get:
86a = $1290
Dividing both sides by 86 gives the price of one apple cheesecake:
a = $15
Substituting the value of a into one of the original equations to find p:
12p + 5($15) = $243
12p + $75 = $243
12p = $243 - $75
12p = $168
p = $14
Therefore, the price of one pecan cheesecake is $14 and one apple cheesecake is $15.