Question 1138242: Someone please help..
Big tipper. On Monday Headley paid $1.70 for two cups of coffee and one doughnut, including the tip. On Tuesday he paid $1.65 for two doughnuts and a cup of coffee, including the tip. On Wednesday he paid $1.30 for one coffee and one doughnut, including the tip. If he always tips the same amount, then what is the amount of each item?
I know how to do the math but I have no idea what the three equations would be... please help
I can’t figure out and I need to show work done with three equations.
Found 2 solutions by Theo, VFBundy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let c equal the cost for one cup of coffee.
let d equal the cost for one doughnut.
let t equal the cost of the tip.
your first equation is 2c + d + t = 1.70
your second equation is c + 2d + t = 1.65
your third equation is c + d + t = 1.30
solve the first and second equations simultaneously to get c - d = .05
solve the second and third equations simultaneously to get d = .35
since c - d = .05, then c must be equal to .4
your solution is that c = .4 and d = .35.
go back to any of the 3 equations and solve for t to get t = .55.
your solution is the price of a cup of coffee is 40 cents and the price of a doughnut is 35 cents and the tip is 55 cents.
i confirmed with all 3 original equations that this solution is correct.
Answer by VFBundy(438)  (Show Source):
You can put this solution on YOUR website! Coffee = c
Doughnut = d
Tip = t
Make three equations:
(1) 2c + d + t = 1.70
(2) c + 2d + t = 1.65
(3) c + d + t = 1.30
(A) From (1), let t = 1.70 - 2c - d
Substitute (A) into (2):
(2) c + 2d + (1.70 - 2c - d) = 1.65
(2) -c + d + 1.70 = 1.65
(2) -c + d = -0.05
(B) From (2), let d = -0.05 + c
Substitute (B) into (A):
(A) t = 1.70 - 2c - (-0.05 + c)
(A) t = 1.70 - 2c + 0.05 - c
(A) t = 1.75 - 3c
(C) From (3), let c = 1.30 - d - t
Substitute (A) and (B) into (C):
(C) c = 1.30 - (-0.05 + c) - (1.75 - 3c)
(C) c = 1.30 + 0.05 - c - 1.75 + 3c
(C) c = -0.40 + 2c
(C) -c = -0.40
(C) c = 0.40
Substitute (C) into (A):
(A) t = 1.75 - 3(0.40)
(A) t = 1.75 - 1.20
(A) t = 0.55
At this point, you have two of the variables solved, c and t, so you can substitute them into any of the original equations to find d. Let's choose equation (1):
(1) 2c + d + t = 1.70
(1) 2(0.40) + d + 0.55 = 1.70
(1) 0.80 + d + 0.55 = 1.70
(1) 1.35 + d = 1.70
(1) d = 0.35
In summary:
Coffee = c = $0.40
Doughnut = d = $0.35
Tip = t = $0.55
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