Question

Castel and Gabriella are selling cheesecakes for a school fundraiser. Customers can buy New York style cheesecakes and apple cheesecakes. Castel sold 14 New York style cheesecakes and 7 apple cheesecakes for a total of $301. Gabriella sold 7 New York style cheesecakes and 10 apple cheesecakes for a total of $274. Find the cost each of one New York style cheesecake and one apple cheesecake.

Answer 1

• $12 and $19

Explanation:

• New York style cheesecakes - x
• Apple cheesecakes - y

We have:

• 14x + 7y = 301
• 7x + 10y = 274

Solve the above system by elimination, double the second equation and subtract the first one:

• 2(7x) + 2(10y) - 14x - 7y = 2(274) - 301
• 14x - 14x + 20y - 7y = 548 - 301
• 13y = 247
• y = 247/13
• y = 19

Find x:

• 14x + 7*19 = 301
• 14x + 133 = 301
• 14x = 301 - 133
• 14x = 168
• x = 168/14
• x = 12