SOLUTION: Larry has 66 music CDs. He has 2 times as many rock CDs as country CDs. He has 3 times as many rock CDs as hip-hop CDs. How many rock CDs does Larry have? Please show me the step

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: Larry has 66 music CDs. He has 2 times as many rock CDs as country CDs. He has 3 times as many rock CDs as hip-hop CDs. How many rock CDs does Larry have? Please show me the step      Log On

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Question 596187: Larry has 66 music CDs. He has 2 times as many rock CDs as country CDs. He has
3 times as many rock CDs as hip-hop CDs.
How many rock CDs does Larry have? Please show me the steps.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of country CD's
Let +b+ = number of rock CD's
+b+=+2a+
+c+ = number of hip-hop CD's
+b+=+3c+
----------------------------
+a+%2B+b+%2B+c+=+66+
+b+=+2a+
+a+=+b%2F2+
and
+b+=+3c+
+c+=+b%2F3+
-----------
By substitution:
+b%2F2+%2B+b+%2B+b%2F3+=+66+
Multiply both sides by 6
+3b+%2B+6b+%2B+2b+=+396+
+11b+=+396+
+b+=+36+
and, since
+a+=+b%2F2+
+a+=+36%2F2+
+a+=+18+
also,
+c+=+b%2F3+
+c+=+36%2F3+
+c+=+12+
Larry has 36 rock CD's
check:
+a+%2B+b+%2B+c+=+66+
+18+%2B+36+%2B+12+=+66+
+66+=+66+
OK