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 = [tex]x[/tex]
Let cost of one apple cheesecake be = [tex]y[/tex]
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 = [tex]3x[/tex]
Cost of 7 apple cheesecake be = [tex]7y[/tex]
Total = $78
We have:
A) [tex]3x+7y=78[/tex]
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 = [tex]12x[/tex]
Cost of 12 apple cheesecake be = [tex]12y[/tex]
Total = $168
We have:
B) [tex]12x+12y=168[/tex]
Dividing each term in equation B by 12.
[tex]\frac{12x}{12}+\frac{12y}{12}=\frac{168}{12}[/tex]
[tex]x+y=14[/tex]
Solving for [tex]x[/tex] in terms of [tex]y[/tex]
Subtracting [tex]y[/tex] both sides.
[tex]x+y-y=14-y[/tex]
[tex]x=14-y[/tex]
Substituting [tex]x=14-y[/tex] in equation A.
[tex]3(14-y)+7y=78[/tex]
Using distribution:
[tex]42-3y+7y=78[/tex]
[tex]42+4y=78[/tex]
Subtracting both sides by 42.
[tex]42+4y-42=78-42[/tex]
[tex]4y=36[/tex]
Dividing both sides by 4.
[tex]\frac{4y}{4}=\frac{36}{4}[/tex]
∴ [tex]y=9[/tex]
Substituting [tex]y=9[/tex] in [tex]x=14-y[/tex]
∴ [tex]x=14-9=5[/tex]
∴ Cost of one New York style cheesecake = $5
∴ Cost of one apple cheesecake = $9
