Answer:
Cost of one New York style cheesecake = $5
Cost of one apple cheesecake = $9
Step-by-step explanation:
Let cost of one New York style cheesecake be = ![x](https://tex.z-dn.net/?f=x)
Let cost of one apple cheesecake be = ![y](https://tex.z-dn.net/?f=y)
Given:
3 New York stile cheesecake and 7 apple cheese cake were sold for a total of $78.
Cost of 3 New York style cheesecake be = ![3x](https://tex.z-dn.net/?f=3x)
Cost of 7 apple cheesecake be = ![7y](https://tex.z-dn.net/?f=7y)
Total = $78
We have:
A) ![3x+7y=78](https://tex.z-dn.net/?f=3x%2B7y%3D78)
12 New York stile cheesecake and 12 apple cheese cake were sold for a total of $168.
Cost of 12 New York style cheesecake be = ![12x](https://tex.z-dn.net/?f=12x)
Cost of 12 apple cheesecake be = ![12y](https://tex.z-dn.net/?f=12y)
Total = $168
We have:
B) ![12x+12y=168](https://tex.z-dn.net/?f=12x%2B12y%3D168)
Dividing each term in equation B by 12.
![\frac{12x}{12}+\frac{12y}{12}=\frac{168}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B12x%7D%7B12%7D%2B%5Cfrac%7B12y%7D%7B12%7D%3D%5Cfrac%7B168%7D%7B12%7D)
![x+y=14](https://tex.z-dn.net/?f=x%2By%3D14)
Solving for
in terms of ![y](https://tex.z-dn.net/?f=y)
Subtracting
both sides.
![x+y-y=14-y](https://tex.z-dn.net/?f=x%2By-y%3D14-y)
![x=14-y](https://tex.z-dn.net/?f=x%3D14-y)
Substituting
in equation A.
![3(14-y)+7y=78](https://tex.z-dn.net/?f=3%2814-y%29%2B7y%3D78)
Using distribution:
![42-3y+7y=78](https://tex.z-dn.net/?f=42-3y%2B7y%3D78)
![42+4y=78](https://tex.z-dn.net/?f=42%2B4y%3D78)
Subtracting both sides by 42.
![42+4y-42=78-42](https://tex.z-dn.net/?f=42%2B4y-42%3D78-42)
![4y=36](https://tex.z-dn.net/?f=4y%3D36)
Dividing both sides by 4.
![\frac{4y}{4}=\frac{36}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B4y%7D%7B4%7D%3D%5Cfrac%7B36%7D%7B4%7D)
∴ ![y=9](https://tex.z-dn.net/?f=y%3D9)
Substituting
in ![x=14-y](https://tex.z-dn.net/?f=x%3D14-y)
∴ ![x=14-9=5](https://tex.z-dn.net/?f=x%3D14-9%3D5)
∴ Cost of one New York style cheesecake = $5
∴ Cost of one apple cheesecake = $9