SOLUTION: The ratio of boys to girls among the students who signed up for a basketball competition is 4 : 3. If 3 boys drop out of the competition and 4 girls join, there will be the same nu

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The ratio of boys to girls among the students who signed up for a basketball competition is 4 : 3. If 3 boys drop out of the competition and 4 girls join, there will be the same nu      Log On


   

Question 967583: The ratio of boys to girls among the students who signed up for a basketball competition is 4 : 3. If 3 boys drop out of the competition and 4 girls join, there will be the same number of boys and girls. How many students have signed up for the basketball competition?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +b%2F+g+=+4%2F3+
(2) +b+-+3+=+g+%2B+4+
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(1) +3b+=+4g+
(1) +b+=+%284%2F3%29%2Ag+
Substitute this result into (2)
(2) +%284%2F3%29%2Ag+-+3+=+g+%2B+4+
(2) +4g+-+9+=+3g+%2B+12+
(2) +g+=+21+
and
(1) +b+=+%284%2F3%29%2Ag+
(1) +b+=+%284%2F3%29%2A21+
(1) +b+=+28+
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+21+%2B+28+=+49+
49 students signed up
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check:
(1) +b%2F+g+=+4%2F3+
(1) +28%2F+21+=+4%2F3+
(1) +4%2F3+=+4%2F3+
and
(2) +b+-+3+=+g+%2B+4+
(2) +28+-+3+=+21+%2B+4+
(2) +25+=+25+
OK