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.

11.25

step-by-step explanation:

juan's ratio of violin to cello is

3/2.5

he practices the violin for 9 hours; this gives us the ratio

9/x

for his cello practice.

together we have the proportion

3/2.5 = 9/x

cross multiplying, 3(x) = 9(2.5)

3x = 22.5

divide both sides by 3:

3x/3 = 22.5/3

x = 7.5

juan practices his cello for 7.5 hours.

nina's ratio of viola to cello is

3/2

since she practiced the cello for the same amount of time as juan, that means she practices 7.5 hours.   this gives us the ratio

x/7.5

and the proportion

3/2 = x/7.5

cross multiplying,

3(7.5) = 2(x)

22.5 = 2x

dividing both sides by 2,

22.5/2 = 2x/2

11.25 = x