9514 1404 393
Answer:
- New York style: $14
- Chocolate Marble: $16
Step-by-step 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.
