Each course at college x is worth either 3 or 4 credits the members of the swim team are taking a total of 49 courses that are worth a total of 161 credits

x= number of credit courses

y = number of 4 credit courses

x+y = 49

solve for x

x=49-y

3x+4y=161

substitute x=49-y into above equation

3(49-y) +4y=161

distribute

147 -3y +4y=161

combine like terms

147+y=161

subtract 147 from each side

y=14

x=49-y

x=49-14

x=35

they took 35 3 credit courses and 14 4 credit courses

35*3+14*4 = 161  so it checks

subtract 147 from each side

If I understand correctly, the question is saying that the rectangles have the same proportions and wants to know the right side length of the smaller rectangle.
If this is the case, then the proportion is 5:3, with 3 being the right side length of the smaller rectangle.
This is because The original is 10:6, which is equal to 5:3.
Also, 5 is half of 10, so to find the right side length, just half the original as well, since you have to do the same to both sides. This results in lengths of 5 and 3.

Hope this helps :)