Answer:
There are 14 blue marbles in the bag.
Explanation:
Let's call the number of green marbles "x". Then we know that the number of red marbles is 112 more than x, or x+112. We can use the ratio to find the number of blue marbles.
First, we need to find the total number of parts in the ratio. That's 12+5+2=19.
Next, we can use the ratio to set up an equation. The number of blue marbles is 2/19 of the total number of marbles. We can write this as:
2/19 (x + x + 112 + blue) = blue
Simplifying this equation, we get:
2x + 224 = 17blue
Now we can solve for blue:
blue = (2x + 224)/17
We know that blue is a whole number, so we need to find a value of x that makes the numerator of this fraction divisible by 17. After some trial and error, we find that x=3 works:
blue = (2(3) + 224)/17 = 14
Therefore, there are 14 blue marbles in the bag.