SOLUTION: On​ Monday, Harold picked up 3 donuts and 6 large coffees for the office staff. He paid 6.75  On​ Tuesday, Melinda picked up 5 donuts and 2 large coffees for the office s

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Question 1192950: On​ Monday, Harold picked up 3 donuts and 6 large coffees for the office staff. He paid 6.75  On​ Tuesday, Melinda picked up 5 donuts and 2 large coffees for the office staff. She paid 4.37  What is the cost of one​ donut? What is the cost of one large​ coffee?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
d and c donuts coffees prices

system%283d%2B6c=6.75%2C5d%2B2c=4.37%29
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Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Informally/mentally....

(1) Divide the first purchase (3 donuts and 6 coffees for $6.75) by 3 to find that the cost of 1 donut and 2 coffees is $2.25.
(2) Compare that to the other purchase of 5 donuts and 2 coffees for $4.37 to see that the cost of the "extra" 4 donuts is $4.37-$2.25 = $2.12
(3) Then determine that the cost of each donut is $2.12/4 = $0.53
(4) Since the cost of 1 donut and 2 coffees is $2.25 and the cost of the donut is $0.53, the cost of the 2 coffees is $2.25-$0.53 = $1.72, so the cost of each coffee is $1.72/2 = $0.86

With formal algebra....

There are an endless number of different ways you could set up and solve this problem using formal algebra. The following method, while perhaps not the easiest way, exactly follows the informal solution described above.

d = cost of a donut
c = cost of a coffee

3d+6c=6.75 (given)
d+2c=2.25 (divide by 3)
5d+2c=4.37 (given)
4d=2.12 (difference between the last two equations)
d=2.12/4=0.53
0.53+2c=2.25
2c=2.25-0.53=1.72
c=1.72/2=0.86