Raven has a bag of 33 red and black marbles. The number of red marbles is 6 more than double the number of black marbles. Let r represent the number of red marbles and b represent the number of black marbles. Which statements about the marbles are true? Check all that apply. The equation r + b = 33 represents the total number of marbles. The equation r = 2 b + 6 can be used to find the number of red marbles. The equation r = 2 b + 6 represents the total number of marbles. The equation r + b = 33 can be used to find the number of red marbles. There are 9 red marbles in the bag. There are 9 black marbles in the bag. There are 24 black marbles in the bag. There are 24 red marbles in the bag.

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If the number of red marbles is 6 more than double the number of black marbles, we can create this equation, with r representing the red marbles and b representing the black marbles.

r=2b+6

We also know that r+b=33, and if we know that r is equal to 2b+6, we can just replace r with that and then solve for b.

2b+6+b=33

We combine like terms.

3b+6=33

We subtract six from both sides.

3b=27

We divide both sides by 3.

b=9

Now we just subtract 9 from 33 to see how many red ones there are.

33-9=24

So, there are 24 red marbles and 9 black marbles.

Now, let's see which of these options are correct.

The equation r+b=33 represents the total number of marbles.

This is true because r plus b is equal to the total, which is 33.

The equation r=2b+6 can be used to find the number of red marbles.

This is true because it we used this r-value to find how many black marbles there were.

The equation r=2b+6 represents the total number of marbles.

This is false because it does not have the total number, which is 33.

The equation r=b=33 can be used to find the number of red marbles.

This is true because we plugged in the r-value to solve for b with this equation.

There are 9 red marbles in the bag.

This is false. There are 24 red marbles.

There are 9 black marbles in the bag.

This is true.

There are 24 black marbles in the bag.

This is false. There are 9 black marbles.

There are 24 red marbles in the bag.

This is true.

Have a wonderful day! :D

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