there are 765 marbles in a in a box. there are twice as many blue marbles as green marbles. there are 3 times as many red marbles as blue marbles, how many red marbles in the box
To find the number of red marbles in the box, we need to follow the given information step by step.
First, let's assign variables to the number of green, blue, and red marbles in the box. Let's say "G" represents the number of green marbles, "B" represents the number of blue marbles, and "R" represents the number of red marbles.
According to the given information, there are twice as many blue marbles as green marbles. So we can write the equation:
B = 2G
Next, it says there are three times as many red marbles as blue marbles. We can write another equation:
R = 3B
Now, we have two equations relating the numbers of marbles. To solve for the variables, we need to use the information that there are 765 marbles in total.
We can express that using the equation:
G + B + R = 765
Now, let's substitute the values of B and R from the previous equations into the total equation:
G + (2G) + (3(2G)) = 765
Simplify:
G + 2G + 6G = 765
Combine like terms:
9G = 765
Divide both sides of the equation by 9:
G = 85
Now, we know the number of green marbles is 85. Since there are twice as many blue marbles, we have:
B = 2G = 2 * 85 = 170
Finally, using the equation R = 3B, we can find the number of red marbles:
R = 3 * B = 3 * 170 = 510
Therefore, there are 510 red marbles in the box.
green marbles --- x
blue marbles --- 2x
red marbles ---- 3(2x) = 6x
x + 2x + 6x = 765
...
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carry on.