Question

7) Rob and Amy are selling cheesecakes for a school fundraiser. Customers can buy New York

style cheesecakes and chocolate marble cheesecakes. Rob sold 11 New York style cheesecakes
and 7 chocolate marble cheesecakes for a total of $266. Amy sold 4 New York style cheesecakes
and 14 chocolate marble cheesecakes for a total of $280. What is the cost each of one New York
style cheesecake and one chocolate marble cheesecake?

Answer 1

9514 1404 393

Answer:

• New York style: $14
• Chocolate Marble: $16

Explanation:

We can let n and c represent the costs of the New York style and the chocolate marble cheesecakes, respectively. Then the two sales are ...

11n +7c = 266 . . . . . . . Rob's sale

4n +14c = 280 . . . . . . Amy's sale

The ratio of coefficients of c is a "nice" number (2), so we can eliminate the c variable easily to solve this. Dividing the second equation by 2 and subtracting it from the first gives ...

(11n +7c) -(1/2)(4n +14c) = (266) -(1/2)(280)

9n = 126 . . . . . . simplify

n = 14 . . . . . . . . divide by 9

Filling this into the first equation, we have ...

11(14) +7c = 266

7c = 112 . . . . . . . . subtract 154

c = 16 . . . . . . . divide by 7

One New York style cheesecake costs $14; one chocolate marble cheesecake costs $16.