SOLUTION: Julie spends 720 minutes per week practicing the piano outside of class. Her ratio of time spent on practicing pieces to time spent on scales and theory is 5 to 3. How many HOURS p

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Julie spends 720 minutes per week practicing the piano outside of class. Her ratio of time spent on practicing pieces to time spent on scales and theory is 5 to 3. How many HOURS p      Log On


   



Question 838999: Julie spends 720 minutes per week practicing the piano outside of class. Her ratio of time spent on practicing pieces to time spent on scales and theory is 5 to 3. How many HOURS per week does she spend on practicing pieces? How many HOURS per week does she spend on scales and theory?
I have used the problem of 5/3=x/y but it gives me another equation.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
First, convert +720+ minutes to hours
( minutes ) x ( hours/minute ) = hours
+720%2A%28+1%2F60+%29+=+12+ hrs
------------------------------
Let +x+ = her time in hours spent on pieces per week
+12+-+x+ = her time in hours spent on scales per week
----------------------------------------------------
+5%2F3+=+x%2F%28+12+-+x+%29+
Multiply both sides by +3%2A%28+12+-+x+%29+
+5%2A%28+12+-+x+%29+=+3x+
+60+-+5x+=+3x+
+8x+=+60+
+x+=+7.5+
+12+-+7.5+=+4.5+
She spends 7 1/2 hours per week on pieces
She spends 4 1/2 hours per week on scales
---------------------
check:
+5%2F3+=+x%2F%28+12+-+x+%29+
+5%2F3+=+7.5%2F4.5+
+5%2A4.5+=+7.5%2A3+
+22.5+=+22.5+
OK