SOLUTION: A 22 inch rope is to be cut into two pieces so that one piece is 6 inches longer than twice the other.How long is each piece if a=2,b=6,and l=22?

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Question 1005835: A 22 inch rope is to be cut into two pieces so that one piece is 6 inches longer than twice the other.How long is each piece if a=2,b=6,and l=22?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the longer piece
+x+=+a%2A%28+l+-+x+%29+%2B+b+
+x+=+a%2Al+-+a%2Ax+%2B+b+
+x+%2B+a%2Ax+=+a%2Al+%2B+b+
+x%2A%28+1+%2B+a+%29+=+a%2Al+%2B+b+
+x+=+%28+a%2Al+%2B+b+%29+%2F+%28+1+%2B+a+%29+
+a+=+2+
+b+=+6+
+l+=+22+
+x+=+%28+a%2Al+%2B+b+%29+%2F+%28+1+%2B+a+%29+
+x+=+%28+2%2A22+%2B+6+%29+%2F+%28+1+%2B+2+%29+
+x+=+50%2F3+
and
+l+-+x+=+22+-+50%2F3+
+l+-+x+=+16%2F3+
------------------
The 2 pieces are 50/3 and 16/3
check:
+x+=+a%2A%28+l+-+x+%29+%2B+b+
+50%2F3+=2%2A%2822+-+x+%29+%2B+6+
+50%2F3+=+44+-+2x+%2B+6+
+50%2F3+=+50+-+2x+
+50+=+150+-+6x+
+6x+=+100+
+x+=+50%2F3+
OK