Question 196881: Please help me justify my answer with 'Algebra'
Mr Dean gives 'Mars Bars' to students that solve his 'Problem of the Day'.
In the last few weeks, this has cost him 18 Mars Bars altogether, no two of the five students who won them received the same number of Mars Bars. However, one clever student got as many as three of the others combined.
How were the Mars Bars distributed amongst the 5 winners?
I know the answer is 1,2,3,4 and 8 but I have to show algebraically that there is only ONE possible solution. How do I do this?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Mr Dean gives 'Mars Bars' to students that solve his 'Problem of the Day'.
In the last few weeks, this has cost him 18 Mars Bars altogether, no two of the five students who won them received the same number of Mars Bars. However, one clever student got as many as three of the others combined.
How were the Mars Bars distributed amongst the 5 winners?
I know the answer is 1,2,3,4 and 8 but I have to show algebraically that there is only ONE possible solution. How do I do this?
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The 5 students are a,b,c,d,e
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e has as many as a,b,and c
a+b+c-e = 0
a+b+c+d+e = 18
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Subtract the 1st eq. from the 2nd to get:
d + 2e = 18
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Then e = (18-d)/2
The (d,e) pairings are (2,8),(4,7),(6,3),(8,1)
But e has to equal a+b+c (none of which are zero).
So e = is 8 or 7
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If e = 7 and d = 4
a+b+c = 7
Then a =1,b=2,c=4 ; but c cannot be the same as d.
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If e = 8 and d = 2
a+b+c = 8
Then a = 1, b = 2, c = 5, d = 2 and e = 8
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Cheers,
Stan H.
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