Jenny decided to grow out her hair. over 6 months, her hair length grew by 100%. during the next 6 months, her hair length grew by 50%. what was the combined increase in hair length during the entire year

150% in 12 months.

In your mind, you could think 100% more is 200% and 50% of that is another 100% so 200% increase. Let's see on paper. x will be her current hair length. 

x + x + .5(x + x) 

x + x is simply her hair length doubling. This is when it grew 100% longer. Then, from that, we have 50% more, so we have to add 50% of the x + x. 

2x + .5x + .5x 
3x 

Subtract our starting length. 

3x - x = 2x 

The difference is 2 hair lengths, or 200% her original length of hair.