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!

We have shown the total amount of marbles and the total ratioThen we proved that taking away one of the BLUE marbles and using the ratio 4:2 will not workNow the most important part, is when we proved that with the specific amount of marbles there can be no ratio

Have Fun Learning!

If you have any questions, please do email me!

Abcd stupid son of a bitxh

Ithink it's the first one ( let me know if it right)