Per package, coffee costs $_____ and tea costs $_____

Question

A coffee shop is having a sale on prepackaged coffee and tea. Yesterday they sold 13 packages of coffee and 44 packages of tea, for which customers paid a total of $394. The day before, 48 packages of coffee and 43 packages of tea was sold, which brought in a total of $738. How much does each package cost?

Answer 1

This problem is set up to force you to do some messy multiplication and division; be careful.

 

13C + 44T = 394

48C+ 43T = 738

 

The easiest and cleanest way to do this problem is to use determinants which you have probably not yet studied.

There are no common factors since both 13 and 43 are prime.

The only way to use elimination is brute force:

Multiply the 1st equation by 48 and the second equation by 13.

Then you will have the same coefficient on C and you can subtract the one equation from the other which will give you an equation in T alone.  Solve that and plug the answer back into either of your original equations to get the value of C.