story problem in need of 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

x = tons of CCC **AND** BBF (can use same variable for both since these amounts[CCC & BBF] are the same)

y = tons of SSS

 

2x+y = 100                         <== tonnage

80x + 65x + 50y = 5810       <== cost

 

   2x +     y = 100   <== multiply all by -50

 145x + 50y =  5810

 

-100x - 50y = -5000

 145x + 50y = 5810

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   45x  +   0   = 810

 

I've done all the heavy lifting, I'll leave the rest to you.  Answers:  18, 18, & 64 tons (label each properly by supplier)