A bag contains only red and blue marbles. There are a total of 21 marbles in the bag. There are 4 red marbles for every 3 blue marbles in the bag. A student removes 1 blue marble from the bag. The student reasons that there are now 4 red marbles in the bag for every 2 blue marbles since 3 - 1 = 2

The student is incorrect, and finding a new ratio is not possible.

Step-by-step explanation:

LET'S UNDERSTAND!!!

Ok, let's establish this first;

The bag has 21 marbles total, with a ratio of 4:3 red:blue marbles.

Now here is a life long trick, 4 + 3 = 7.

Now do 21 / 7 = 3.

So three of ratio groups.

This also shows there are 12 red marbles and 9 blue marbles total or the total ratio is 12:9.

Now that we understand this we will go to the next step.

NEXT STEP: Is it true?

Then a student takes out a BLUE marble. Leaving 20 marbles left.

The total amount of red marbles is 12 (it stays the same) and the total of blue marbles is 9 - 1 = 8.

Now, they say the ratio is 4:2 red:blue.

(The total ratio will be )

Although, if we multiply by 3 we get 12:6 (totaling 18 marbles). If we try to multiply by 4 we get 16:8 (totaling 24 marbles). So, this shows that the ratio would not give you 20 marbles.

NEXT STEP: Find the correct ratio!

Alright, moving back the beginning of the problem.

Remember we have a total of 20 marbles our ratio now 12:8.

We will look at common factors. Their common factors (of 8 and 12) are 1, 2 and 4; and 4 is the largest common factor.

Now to see if the new ratio can be proven, to obtain 8 and 12 multiplying by 4 will take 2 times for 8 and 3 times. This will not work.

Looking at 2 we all know that won't work as well as 1. Therefore this shows this specific amount of marbles cannot be proven be any ratio!

COMPLETE CONCLUSION:

Alright so what have we proven? Let's take a look!

Have Fun Learning!

If you have any questions, please do email me!

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step-by-step explanation:

8+8+6+6