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

Algebra.Com
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)   (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 =  =  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.



RELATED QUESTIONS

Problem: The students from algebra class go for coffee together every day at 9:00 AM. On (answered by mangopeeler07)
Hello, Can someone please help me with this math I am having a hard time with it. it... (answered by stanbon)
Systems of Equations and Inequalities i) Problem: The students from algebra class go for (answered by stanbon)
Will you please help me with this problem? Write a system of two equations in two... (answered by ptaylor)
Will you please help me with this problem? Write a system of two equations in two... (answered by stanbon)
Write a system of two equations in two unknowns. Solve the system by using the addition... (answered by checkley77)
Write a system of two equations in two unknowns. On Monday, Archie paid $3.40 for three... (answered by Cromlix)
At a local bakery, the price for a doughnut is $0.85. Each day the manager of the store... (answered by josmiceli)
The number of persons entering a building at 10:00 a.m one day was 235 more than that of... (answered by ikleyn)