Answer:
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 ratio
- Then we proved that taking away one of the BLUE marbles and using the ratio 4:2 will not work
- Now the most important part, is when we proved that with the specific amount of marbles there can be no ratio
Have Fun Learning!
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