You have decided to give your best friend a bag of red and green marbles for his birthday. your friend
likes green marbles better than red ones, so the
bag has twice as many green marbles as red. The
label on the bag says it lcontains a total of 84 marbles.
How many green marbles are in the bag? Write a
System of equations for this problem. Then solve the
problem using any method you like. Be sure to check
your solutions

There are 28 red marbles and 56 green marbles in the bag.

Step-by-step explanation:

Let's define:

R = number of red marbles in the bag.

G = number of green marbles in the bag.

We know that:

"There is a total of 84 marbles in the bag"

Then we can write this as:

R + G = 84

"The bag has twice as many green marbles as red marbles"

Then:

G = 2*R

So we have two equations:

R + G = 84

G = 2*R

This is the system of equations we need to solve.

To solve this, we usually start by isolating one of the variables in one of the equations, here we can see that G is already isolated in the second equation, then we can ignore the first step.

Now that we have an isolated variable, we can replace it in the other equation, then we can replace the second equation in the first one to get:

R + G = 84

R + (2*R) = 84

3*R = 84

R = 84/3 = 28

This means that there are 28 red marbles in the bag.

Now we can use the equation:

G = 2*R

To find the number of green marbles, where we need to replace R y 28, then we get:

G = 2*28 = 56

Which means that there are 56 green marbles.