SOLUTION: A box of gems is found on a treasure hunt. There are 2 diamonds or every 3 rubies. There are 5 sapphires for every diamond. If a total of 30 gems are in the box, how many are sapph

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Question 882378: A box of gems is found on a treasure hunt. There are 2 diamonds or every 3 rubies. There are 5 sapphires for every diamond. If a total of 30 gems are in the box, how many are sapphires?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +d%2Fr+=+2%2F3+
(2) +s%2Fd+=+5%2F1+
(3) +d+%2B+r+%2B+s+=+30+
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(1) +r%2Fd+=+3%2F2+
Divide both sides of (3) by d
(3) +1+%2B+r%2Fd+%2B+s%2Fd+=+30%2Fd+
and, from (1) and (2):
(3) +1+%2B+3%2F2+%2B+5+=+30%2Fd+
(3) +15%2F2+=+30%2Fd+
(3) +d+=+4+
and
(2) +s%2Fd+=+5+
(2) +s+=+5d+
(2) +s+=+5%2A4+
(2) +s+=+20+
The are 20 sapphires
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check:
(1) +r%2Fd+=+3%2F2+
(1) +r+=+%283%2F2%29%2A4+
(1) +r+=+6+
and
(3) +d+%2B+r+%2B+s+=+30+
(3) +4+%2B+6+%2B+20+=+30+
(3) +30+=+30+
OK