Beth and pranav are selling cheesecakes for a school fundraiser. customers can buy new york
style cheesecakes and apple cheesecakes. beth sold 3 new york style cheesecakes and 7 apple
cheesecakes for a total of $78. pranav sold 12 new york style cheesecakes and 12 apple
cheesecakes for a total of $168. find the cost each of one new york style cheesecake and one
apple cheesecake.

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 =

Let cost of one apple cheesecake be =

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 =

Cost of 7 apple cheesecake be =

Total = $78

We have:

A)

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 =

Cost of 12 apple cheesecake be =

Total = $168

We have:

B)

Dividing each term in equation B by 12.

Solving for in terms of

Subtracting both sides.

Substituting in equation A.

Using distribution:

Subtracting both sides by 42.

Dividing both sides by 4.

∴

Substituting in

∴

∴ Cost of one New York style cheesecake  = $5

∴ Cost of one apple cheesecake = $9

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents