Anne Barry and Cathy enter a coffee shop Anne orders two cof

Anne, Barry, and Cathy enter a coffee shop. Anne orders two coffees, one juice, and two doughnuts and pays $8.75. Barry orders one coffee and three doughnuts and pays $4.50. Cathy orders three coffees, one Juice, and four doughnuts and pays $12.50. Find the price of coffee, Juice, and doughnuts at this coffee shop. coffee $ _____ juice $ _____ doughnuts $ _____

Solution

2c + j + 2d = 8.75

c + 3d = 4.50

3c + j + 4d = 12.50

Eliminating j from equations 1 and 3 :
(3c + j + 4d) - (2c + j + 2d) = 12.50 - 8.75

c + 2d = 3.75

Now, from
c + 2d = 3.75
c + 3d = 4.50

Subtracting :
d = 0.75

And thus, c + 2(0.75) = 3.75
c + 1.50 = 3.75
c = 2.25

Andthen :
2c + j + 2d = 8.75

2(2.25) + j + 2(0.75) = 8.75

j = 2.75

So, we have :
c = 2.25
j = 2.75
d = 0.75