SOLUTION: On MOnday, Harold picked up six donuts and 2 large coffees for the office staff. He paid $5.74. On Tuesday, Melinda picked up 3 donuts and 5 large coffee for the office staff. She

Algebra ->  Systems-of-equations -> SOLUTION: On MOnday, Harold picked up six donuts and 2 large coffees for the office staff. He paid $5.74. On Tuesday, Melinda picked up 3 donuts and 5 large coffee for the office staff. She       Log On


   

Question 1048809: On MOnday, Harold picked up six donuts and 2 large coffees for the office staff. He paid $5.74. On Tuesday, Melinda picked up 3 donuts and 5 large coffee for the office staff. She paid $7.17. what is the cost of 1 donut? What is the cost of 1 large coffee?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
d = number of donuts.
c = number of large coffee.

your equations are.

6d + 2c = 5.74
3d + 5c = 7.17

multiply both sides of the second equation by 2 to get and leave the first equation alone to get:

6d + 2c = 5.74
6d + 10c = 14.34

subtract the first equation from the second to get:

8c = 8.60

divide both sides of this equation by 2 to get:

c = 1.075

replace c with 1.075 in the first eqution and solve for d.

start with 6d + 2c = 5.74
replace c with 1.075 to get 6d + 2 * 1.075 = 5.74
simplify to get 6d + 2.15 = 5.74
solve for d to get d = (5.74 - 2.15) / 6
this makes d = .59833333.....

you have:

c = 1.075
d = .59833333.....

replace c and d in both equations to see if both equations hold true.

first equation becomes 6d + 2c = 5.74 which becomes 6 * .59833333..... + 2 * 1.075 = 5.74 which becomes 5.74 = 5.74 which confirms the first equation is true.

second equation becomes 3d + 5c = 7.17 which becomes 3 * .59833333..... + 5 * 1.075 = 7.17 which becomes 7.17 = 7.17 which confirms the second equation is true.

both equations are true when c = .59833333..... and d = 1.075 so the solution looks good.

in my opinion, this problem is not very realistic.

i've never see a cup of coffee cost a fraction of a penny and i've never seen a donut cost a fraction of a penny.

despite that, the mathematics works out and that's your solution.

it's possible you copied the numbers wrong.
if so, then duplicate the solution method using the right numbers and you should be ok.