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.

Part A) How many of each color marble are in the bag?

Part B) A student removes 1 blue marble from the bag. The student reasons that the ratio of red to blue marbles is now 5:3 since 4 - 1 = 3.
Explain the error in the student's reasoning.
Compute the correct ratio of red to blue marbles after 1 blue marble is removed.

Answer 1

The ratio computed shows that the student's reasoning that there are now 5 red marbles in the bag for every 3 marbles is incorrect.

How to illustrate the ratio?

From the information given, there are 36 marbles in the bag. The number of red marbles will be:

= 5/9 × 36

= 20 marbles

The number of blue marbles will be:

= 4/9 × 36

= 16 marbles

When a student removes 1 blue marble from the bag, the number of blue marbles will be:

= 16 - 1

= 15 marbles.

Therefore, the ratio of red to blue marbles will be:

= 20:15 = 4:3

Therefore, the student's reasoning that there are now 5 red marbles in the bag for every 3 marbles is incorrect.