SOLUTION: On the first day of a two day meeting, 10 coffees and 10 doughnuts were purchased for a total of $20.00. Since nobody drank the coffee and all the doughnuts were eaten, the next da

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Question 1145714: On the first day of a two day meeting, 10 coffees and 10 doughnuts were purchased for a total of $20.00. Since nobody drank the coffee and all the doughnuts were eaten, the next day only 2 coffees and 14 doughnuts were purchased for a total of $13.00. How much did each coffee and each doughnut cost?
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

First appearance of the system


    10x + 10y = 20    (1)

     2x + 14y = 13    (2)


Multiply equation (2) by 5 (both sides).  Keep equation (1) as is.

Second appearance of the system


    10x + 10y = 20    (1')

    10x + 70y = 65    (2')


Now subtract equation (1') from equation (2').  The terms "10x" will cancel each other (ELIMINATION !), and you will get


          60y = 45,

            y = 45%2F60 = 3%2F4 of the dollar = $0.75.


Next substitute y = 0.75 into equation (1') to get

     10x = 20 - 10*0.75 = 12.50,

       x = 1.25.


ANSWER.  The price for each coffee is $1.25;  for each doughnut $0.75.