Final answer:
To find the cost of one pecan cheesecake and one strawberry cheesecake, we can set up a system of equations using the given information. By solving the system of equations, we can determine that the cost of one pecan cheesecake is $5 and the cost of one strawberry cheesecake is $10.
Step-by-step explanation:
Let's assume the cost of one pecan cheesecake is 'p' dollars and the cost of one strawberry cheesecake is 's' dollars.
From the given information, Stephen sold 4 pecan cheesecakes and 1 strawberry cheesecake for a total of $30, so we can write the equation: 4p + 1s = 30.
Natalie sold 2 pecan cheesecakes and 1 strawberry cheesecake for a total of $20, so we can write the equation: 2p + 1s = 20.
Now we have a system of equations:
We can solve this system of equations to find the values of 'p' and 's', which will give us the cost of one pecan cheesecake and one strawberry cheesecake.
By subtracting the second equation from the first equation, we get: (4p + s) - (2p + s) = 30 - 20, simplifying to 2p = 10.
Dividing both sides of the equation by 2, we can find that p = 5.
Substituting the value of p into one of the original equations, we get: 4(5) + s = 30, simplifying to 20 + s = 30.
Subtracting 20 from both sides of the equation, we find that s = 10.
Therefore, the cost of one pecan cheesecake is $5 and the cost of one strawberry cheesecake is $10.