Assistance on math word problem

(Question)

There are a yellow flask and a red flask. The yellow flask contains more than one cup of yellow paint, and the red flask contains an equal amount of red paint. One cup of the red paint in the red flask is poured into the yellow flask and mixed thoroughly. Then one cup of the paint mixture in the yellow flask is poured into the red flask and mixed thoroughly.

A.Without doing any calculations, which do you think will be greater, the percentage of yellow paint in the red flask or the percentage of red paint in the yellow flask? (explain reasoning)

B.Now use calculations to figure out the answer to the problem in part A. Work with specific quantities of yellow and red paint. (Remember, both flasks have the same amount at the start, and both contain more than one cup.) Draw picures to help you calculate the quantities and percentages after the mixing occurs. Do you get a different answer than you got in part A? If so, reconcile your answers

Re: Assistance on math word problem

Let y be the amount of paint in the yellow flask, r be the amount of paint in the red flask in cups. We are given y = r. I'm going to skip to B since A is interpretation.

B. Let y = r = 2. (simple enough number to use)

If one cup of red paint is mixed thoroughly into the yellow flask, we have that y = 3, with $\displaystyle \frac{1}{3}$ part red paint $\displaystyle \frac{2}{3}$ part yellow paint and r = 1, 1 cup red paint.

If one cup of mixed paint from the mixed paint from the yellow flask is mixed into the red flask, we have that y = 2, with $\displaystyle \frac{1}{3}$ part red paint $\displaystyle \frac{2}{3}$ part yellow paint (concentration doesn't change given it was mixed thoroughly) and r = 2, with the following concentration.

1 cup + 1/3 cup red paint, 2/3 cup yellow paint (out of 2 cups). Hence the concentration of red paint is $\displaystyle \frac{\frac{4}{3}}{2} =\frac{2}{3}$ and the concentration of yellow paint is $\displaystyle \frac{\frac{2}{3}}{2}} = \frac{1}{3}$

Re: Assistance on math word problem