Juan and Nina are in the Junior High Orchestra. As part of the orchestra they each have to learn two instruments. Juan is learning to play the violin and the cello. For every 3 hours that Juan spends practicing the violin he practices the cello for 2.5 hours. Nina is learning to play the viola and cello. For every 3 hours Nina spends practicing the viola she practices the cello for 2 hours.

If Juan practiced the violin for 9 hours last week and Juan and Nina practiced the cello for the same amount of time, then Nina practiced the viola for
hours last week.

Question

Juan and Nina are in the Junior High Orchestra. As part of the orchestra they each have to learn two instruments. Juan is learning to play the violin and the cello. For every 3 hours that Juan spends practicing the violin he practices the cello for 2.5 hours. Nina is learning to play the viola and cello. For every 3 hours Nina spends practicing the viola she practices the cello for 2 hours.

If Juan practiced the violin for 9 hours last week and Juan and Nina practiced the cello for the same amount of time, then Nina practiced the viola for 
 hours last week.

supie · Answer

So Juan spent 9hrs practicing his violin last week. 3:2.5 (The ratio of the amount of hours spent practicing the violin and cello, I could also write it as for every 3 hours Juan practices the violin, he practices 2.5 for the cello.) So, 3hrs violin to 2 1/2 hrs cello and 9hrs violin to ?hrs cello We can replace what we don't know (need to find) with x So $$3x=9(2.5)$$$$x=?$$ Same rule goes for Nila just with different numbers. 3hrs v. 2hrs c. This time we don't know how much the violin is so x hrs v. 7.5 hrs c. $$2x=3(7.5)$$$$x=7.5(1.5)\ x=?$$