Let's start with our knowns:
1. We know there are only green and orange marbles in the bag.
2. The number of green marbles is five times the number of orange marbles.
3. The total number of marbles in the bag is 594.
We need to find the number of each color of marble in the bag. So let's define a variable for each color:
Let's call the number of green marbles 'g'.
And, let's call the number of orange marbles 'o'.
Now we have two variables, and we'll use them to set up two equations based on the facts we know:
Firstly, because the number of green marbles is five times the number of orange marbles, we can write this equation:
g = 5o
Secondly, the total number of marbles in the bag is 594. So the sum of green and orange marbles should be equal to this number. This gives us our second equation:
g + o = 594
Now that we have two equations, we can use them to solve for our variables.
We can substitute the first equation (g = 5o) into the second equation, replacing 'g' with '5o':
5o + o = 594
This equation simplifies to:
6o = 594
Then, divide each side by 6 to solve for 'o':
o = 594 / 6
The solution tells us that there are 99 orange marbles in the bag.
Now, let's find the number of green marbles. Going back to our first equation (g = 5o), substitute 'o' with its value of 99:
g = 5 * 99
This equation tells us that there are 495 green marbles.
To check our solution, we can add the number of green marbles and orange marbles together. If the sum equals 594, our total number of marbles, then we can confidently say our solution is correct.
Let's check:
495 + 99 = 594
Our check confirms our solution is correct - there are 495 green marbles and 99 orange marbles in the bag.