Answer:
One pecan cheesecake = $9
One apple cheesecake = $20
Explanation:
This is a system of equations problem, so we can set up these equations (Note: p = pecan cheesecake cost | a = apple cheesecake cost):
8p + 12a = 312
9p + 6a = 201
Now, we can solve the system of equations. Below is an example of using the elimination method to solve the system:
1. 8p + 12a = 312 --> -4p - 6a = -156
9p + 6a = 201 --> 9p + 6a = 201
2. 5p = 45
3. p = 9
4. 8(9) + 12a = 312
72 + 12a = 312
12a = 240
a = 20
1. We try to make one of the terms equal to the negative version of the other term to eliminate that term; here, I am eliminating "a". To do this, find a multiple of one of the equations where one of the terms is the negative version of the other term. In other words, divide/multiply the equation by a number so one of the terms in the equation is the negative version of the term in the other equation (I divided the first equation by -2 so 12a becomes -6a, the negative version of 6a in the second equation.
2. Next, add the two equations' corresponding terms
(-4p + 9p = 5p; -6a + 6a = 0; -156 + 201 = 45)
3. Simplify the equation (5p = 45; p = 45/5; p = 9)
4. Substitute the term you found back into one of the equations to find the other term.