A box is filled with green marbles, red marbles, and blue marbles. The ratio of red marbles to green marbles is 3:1. The ratio of green marbles to all of the marbles in the box is 2:11. Write each of the following ratios using the symbol. The ratio of red marbles to blue marbles.

  red : blue = 2 : 1

Step-by-step explanation:

It is convenient to write the ratios so that the number representing green marbles is the same in both cases.

  red : green = 3 : 1 = 6 : 2

Then we have ...

  red : green : total = 6 : 2 : 11

The number of ratio units for blue marbles is then 11 -6 -2 = 3, so we have ...

  red : green : blue : total = 6 : 2 : 3 : 11

Then red : blue = 6 : 3 = 2 : 1