story problem help

Question

A bagel store orders cream cheese from three suppliers, Cheesy Cream Corp. (CCC), Super Smooth & Sons (SSS), and Bagel's Best Friend Co. (BBF). One month, the total order of cheese came to 100 tons (they do a booming trade). The costs were $80, $50 and $65 per ton from the three suppliers respectively, with the total cost amounting to $5,810. Given that the store ordered the same amount from CCC and BBF, how many tons of cream cheese were ordered from each supplier?

Answer 1

Let c = tons of CCC cheese, s = tons of SSS cheese, and b = tons of BBF cheese. You can write a system of equations to solve this problem:

 

c + s + b = 100

80c + 50s + 65b = 5810

c = b

 

Substitute the third equation into the first equation for c. Then, solve the first equation for s. Plug that expression for s into the second equation, and plug the third equation into the second equation for c as well. You should be able to solve for b, which equals c, and use that information to solve for s.