Is there a connection between rate and slope?

Apositive number a or the same number a increased by 50% and then decreased by 50% of the result?

Jack has a piece of red ribbon that is two times as long as his piece of blue ribbon. he says that he can use two different equation to find out how long his piece of red ribbon is compared to his piece of blue ribbon is. is he correct? explain his reasoning

Someone answer this check out the image!