Question 123287
"a group of friends eat at a restaurant and agreed to split the $6.00 bill equally. Two men left without paying and the remaining others were assessed .25 more. How many men in the party originally?"
It seems like a linear equation that has 2 variables. How much did each spend and how many men.
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Assume there were originally "x" men.
Since the bill was $6 each man would have owed 6/x dollars
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But two left so there were only "x-2" men.
The bill was still $6 so each would have to pay 6/(x-2) dollars
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The latter payment was $0.25 more than the former:
EQUATION:
6/(x-2) - 6/x = 0.25
Divide thru b 6 to get:
1/(x-2) - 1/x = 0.0417
[x-(x-2)] = 0.0417x(x-2)
2 = 0.0417x(x-2)
x(x-2) = 48
x^2-2x-48=0
(x-8)(x+6)=0
Positive answer:
x = 8 (This the original number of men in the group)
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Cheers,
Stan H.