SOLUTION: Quinn, Rhonda, and Sue shared 3/4 of a whole pizza. Quinn was hungrier than Rhonda and ate twice as much as Rhonda did. Sue ate 3/4 as much as Rhonda. What part of the whole pizza

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Quinn, Rhonda, and Sue shared 3/4 of a whole pizza. Quinn was hungrier than Rhonda and ate twice as much as Rhonda did. Sue ate 3/4 as much as Rhonda. What part of the whole pizza       Log On


   

Question 879522: Quinn, Rhonda, and Sue shared 3/4 of a whole pizza. Quinn was hungrier than Rhonda and ate twice as much as Rhonda did. Sue ate 3/4 as much as Rhonda. What part of the whole pizza did each eat?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +q+ = Quinn's share
Let +r+ = Rhonda's share
Let +s+ = Sue's share
------------------------
(1) +q+%2B+r+%2B+s+=+3%2F4+
(2) +q+=+2r+
(3) +s+=+%283%2F4%29%2Ar+
------------------
Substitute (2) and (3) into (1)
(1) +2r+%2B+r+%2B+%283%2F4%29%2Ar+=+3%2F4+
(1) +3r+%2B+%283%2F4%29%2Ar+=+3%2F4+
(1) +12r+%2B+3r+=+3+
(1) +15r+=+3+
(1) +r+=+1%2F5+
and
(2) +q+=+2r+
(2) +q+=+2%2A%281%2F5%29+
(2) +q+=+2%2F5+
and
(3) +s+=+%283%2F4%29%2Ar+
(3) +s+=+%283%2F4%29%2A%281%2F5%29+
(3) +s+=+3%2F20+
------------------
Quinn's share is 2/5
Rhonda's share is 1/5
Sue's share is 3/20
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check:
(1) +q+%2B+r+%2B+s+=+3%2F4+
(1) +2%2F5+%2B+1%2F5+%2B+3%2F20+=+3%2F4+
(1) +8%2F20+%2B+4%2F20+%2B+3%2F20+=+15%2F20+
(1) +15%2F20+=+15%2F20+
OK