SOLUTION: James, Ashley, and Nicole, all siblings visiting scene 75, have collectively won a total of 340 redemption prize points. Their mother, Kathy, decides how the points will be split a

Question 971296: James, Ashley, and Nicole, all siblings visiting scene 75, have collectively won a total of 340 redemption prize points. Their mother, Kathy, decides how the points will be split amongst the three children. She says James and Ashley behaved very poorly today, though James behaved even worse than Ashley. Kathy asks you to split the points such that James receives 40 points fewer than Ashley and Ashley receives 80 points fewer than Nicole. How many points does each child receive?
Found 3 solutions by stanbon, checkley77, josmiceli:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
James, Ashley, and Nicole, all siblings visiting scene 75, have collectively won a total of 340 redemption prize points. Their mother, Kathy, decides how the points will be split amongst the three children. She says James and Ashley behaved very poorly today, though James behaved even worse than Ashley. Kathy asks you to split the points such that James receives 40 points fewer than Ashley and Ashley receives 80 points fewer than Nicole. How many points does each child receive?
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Nicole points:: x
Ashley points:: x-80
James points::: x-80-40 = x-120
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Equation::
x + x-80 + x-120 = 340
3x - 200 = 340
3x = 540
x = 180 points (Nicole's #)
x-80 = 100 points (Ashley's #)
x-120 = 60 points (James's #)
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Cheers,
Stan H.
Answer by checkley77(12844)   (Show Source): You can put this solution on YOUR website!
J=A-40
A=N-80
J+A+N=340
J + A + N
(A-40)+(N-80)+N=340
A+2N-120=340
A
(N-80)+2N-120=340
3N-200=340
3N=340+200
3N=540
N=540/3
N= 180 POINTS FOR NICOLE.
A=180-80=100 POINTS FOR ASHLEY.
J=100-40=60 POINTS FOR JAMES.
PROOF:
60+100+180=340
340=340
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
(1)
(2)
(3)
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(3)
(3)
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Substitute (2) and (3) into (1)
(1)
(1)
(1)
(1)
(1)
and
(2)
(2)
(2)
and
(3)
(3)
(3)
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James gets 60
Ashley gets 100
Nicole gets 180
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check:
(1)
(1)
(1)
OK

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