Your a 7th grade math teacher and you want to create an experiment for your class with red, yellow and purple marbles in a bag. You want to theoretical probability of drawing a red marble to be 1/2, the theoretical probability of drawing a yellow to be 1/2, and the theoretical probability of drawing a purple to also be 1/6. If you want a total of 1260 marbles in the bag: How many red marbles are you going to put in bag?

well, since P(red)=1/2, you need

red/1260 = 1/2

14 units, x-5/2=y-7/3=z-3/6

ggi

To solve this problem, we'll need to set up a system of equations based on the given probabilities and the total number of marbles. We'll use the following variables:

Let "r" represent the number of red marbles.
Let "y" represent the number of yellow marbles.
Let "p" represent the number of purple marbles.

We know that the theoretical probability of drawing a red marble is 1/2. This means that the ratio of red marbles to the total number of marbles is 1/2. Therefore, the equation is:

r / (r + y + p) = 1/2

We also know that the theoretical probability of drawing a yellow marble is 1/2. This means the ratio of yellow marbles to the total number of marbles is also 1/2. So our second equation is:

y / (r + y + p) = 1/2

Lastly, the theoretical probability of drawing a purple marble is 1/6. This means the ratio of purple marbles to the total number of marbles is 1/6. Our third equation is:

p / (r + y + p) = 1/6

Now, we can solve this system of equations for the number of red marbles.

First, let's use the equation for the probability of drawing a red marble to eliminate the denominators:

2r = r + y + p

Next, let's rearrange the equation to simplify:

r = y + p

Now, let's substitute this equation into the other two equations:

y / (2r) = 1/2

p / (2r) = 1/6

Now, let's simplify these equations:

2y = r

6p = 2r

Substitute the value of r from the first equation into the second equation:

6p = 2y

Now, rearrange this equation to solve for y:

y = 3p

Substitute this value of y into the equation r = y + p:

r = 3p + p

Simplify:

r = 4p

Now, we have a relationship between r and p. The value of p must be a multiple of 4, and the value of r must be 4 times the value of p.

Given that the total number of marbles is 1260, we can set up a final equation for the sum of the marbles:

r + y + p = 1260

Substitute the values of r and y:

4p + 3p + p = 1260

Simplify:

8p = 1260

Divide both sides by 8:

p = 157.5

Since we can't have a fraction of a marble, p must be a whole number. The closest whole number to 157.5 is 158.

Therefore, you would put 158 red marbles in the bag to satisfy the given probabilities and the total number of marbles.