Question 1044759: A violinist is learning a waltz and a sonatina. One day she practices for 33 minuts by playing the waltz 4 times amd the sonatina 3 times. The next day she plays the waltz 6 times and the sonatina only once, for the total of 25 minutes. Using algebraic method, determine the length of each piece.
Answer by ikleyn(52768)   (Show Source):
You can put this solution on YOUR website! .
A violinist is learning a waltz and a sonatina. One day she practices for 33 minutes by playing the waltz 4 times and the sonatina 3 times.
The next day she plays the waltz 6 times and the sonatina only once, for the total of 25 minutes. Using algebraic method,
determine the length of each piece.
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Let "w" be the length of the waltz and "s" be that of the sonata, in minutes.
Then you have these two equations
4w + 3s = 33, (1)
6w + s = 25. (2)
From (2), express s = 25 - 6w and hen substitute it into (1). You will get
4w + 3*(25-6w) = 33, or
4w + 75 - 18w = 33, or
-14w = 33-75,
-14w = 42,
w =  = 3.
Answer. 3 minute for the waltz and 25-6w = 25-18 = 7 minutes for the sonatina.
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