Percentage of fish with stripes

Question

The question I’m trying to solve:

The percentage of fishes in a tank with stripes is 45%. The fish have either red or blue stripes, or both. Of the fishes with stripes, 70% have red stripes and 50% have blue stripes. What percentage of all the fishes have: i) Red stripes ii) Blue stripes iii) Blue and red stripes.

For the first I multiplied 45% and 70% to obtain 31.5%. However I’m not sure if this is correct because of the 70% of the fish with red stripes some of them will also have blue stripes. And for the second part I simply used my 31.5% and subtracted it from the 45% to obtain the percentage of the fish who do not have red stripes (i.e. they have blue stripes) and I got 13.5%. Again, I’m not sure if this is correct either because I’m assuming that 31.5% have red stripes. I’m also not sure because I could have found out the percentage of fish with blue stripes in a similar way to part i) (i.e. multiply 45% by 50%) and I would have obtained a different answer. Now for the third part I said that the percentage of fish with blue stripes must be the difference of all the fish with stripes and 100%. I obtained 70%+50% -100%= 20%. But again I’m not sure of my logic here is right.

Answer 1

You are oscillating between the meaning of having some particular color of stripes. You have the following categories: a) blue stripes only, b) red stripes only, c) both blue and red. In addition, in the problem appear d) blue stripes which is a+c, and e) red stripes, which is b+c.

Now look at the striped fish only. 70% have red stripes. That is category e. That means 30% have blue only (a). 50% have blue stripes (d), meaning that red only (b) is 50%. You can conclude now that 20% have both color stripes.

This should be enough to lead you to the answer

Answer 2

You don't have enough information to determine the intersection of fish with red and blue stripes. Knowing the total number of fish in the tank would help. Let's call that $N$.

Then $.45N = 70 + 50 - 2RB$ where $RB$ is the number of fish with both red and blue stripes.

Therefore $RB = 60 - .225N$

i) Just red striped fish $R = 70 - RB$

ii) Just blue striped fish $B = 50 - RB$

iii) Both red and blue $= RB$