Question 1138242
Coffee = c
Doughnut = d
Tip = t
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Make three equations:
(1) 2c + d + t = 1.70
(2) c + 2d + t = 1.65
(3) c + d + t = 1.30
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(A) From (1), let t = 1.70 - 2c - d
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Substitute (A) into (2):
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(2) c + 2d + (1.70 - 2c - d) = 1.65
(2) -c + d + 1.70 = 1.65
(2) -c + d = -0.05
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(B) From (2), let d = -0.05 + c
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Substitute (B) into (A):
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(A) t = 1.70 - 2c - (-0.05 + c)
(A) t = 1.70 - 2c + 0.05 - c
(A) t = 1.75 - 3c
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(C) From (3), let c = 1.30 - d - t
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Substitute (A) and (B) into (C):
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(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
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Substitute (C) into (A):
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(A) t = 1.75 - 3(0.40)
(A) t = 1.75 - 1.20
(A) t = 0.55
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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):
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(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
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In summary:
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Coffee = c = $0.40
Doughnut = d = $0.35
Tip = t = $0.55