What is the correct ration of red to blue marbles after the student draws 1 blue marble?

Question

A bag contains only red and blue marbles. There are a total of 36 marbles in the bag. There are 5 red marbles for every 4 blue marbles in the bag. A Student removes 1 blue marble from the bag. The student reasons that there are now 5 red marbles in the bag for every 3 blue marbles since 4-1=3. What is the correct ration of red to blue marbles after the student draws 1 blue marble?

Answer 1

Well, for only one set of 9 marbles (that used to be 5 red to 4 blue) the ratio is now 5:3.  But what about all the others?

 

However, there were a total of 36 marbles initially.  That is, 20 red and 16 blue, or a ratio of 5:4.

 

Now, there are 20 red to 15 blue, or 20:15, which reduces to 4:3.

Answer 2

Watch out...what the student thinks is a "red herring"!

 

Let R = red marbles and B = blue

 

R + B = 36

5(B/4) = R

 

5(B/4) + B =36

9B/4 = 36

B/4 = 4 => B =16 and R = 20

 

B-1 =15 and R/B =  20/15 = 4/3