Samuel bought a jacket for $16 in january. the cost of the jacket increased to $24 in september. what percent of the original price is the new price?

Write a proportion first, change over original, like this:
 8      x
16   100
(I got 8 because the difference between 24 and 16 is 8 and I got 100 because percents are out of 100.)
Cross multiply 8 by 100 and you get 800.
Divide 800 by 16 and you get 50.
It changed by 50%