SOLUTION: Algebra: Judy and Linda decided to shre the cost of a $21.00 pizza based on how much eat ate. If Judy ate 3/4 of the amount that Linda ate, how much should each pay?

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Question 643808: Algebra: Judy and Linda decided to shre the cost of a $21.00 pizza based on how much eat ate. If Judy ate 3/4 of the amount that Linda ate, how much should each pay?
Answer by kevwill(135) About Me  (Show Source):
You can put this solution on YOUR website!
Let J be the fraction of the pizza that Judy ate and L be the fraction of the pizza that Linda ate. Since Judy ate 3/4 the amount that Linda ate,
J+=+%283%2F4%29%2AL
And since we assume that together they ate the whole pizza,
J+%2B+L+=+1
Substituting:
%283%2F4%29%2AL+%2B+L+=+1
%283%2F4%29%2AL+%2B+%284%2F4%29%2AL+=+1
%28%283%2B4%29%2F4%29%2AL+=+1
%287%2F4%29%2AL+=+1
%284%2F7%29%2A%287%2F4%29%2AL+=+%284%2F7%29%2AL
L+=+4%2F7
So Linda ate 4%2F7 of the pizza and Judy ate 3%2F7 of the pizza.
Therefore Linda should pay 21%2A%284%2F7%29 = $12.00 and Judy should pay 21%2A%283%2F7%29 = $9.00.