A box contains an assortment of 100 coloured marbles, coloured red, blue and green. The ratio of blue balls to green balls is 1:3. If there are 16 red balls in the box, what is the ratio of red balls to green balls, and red balls to blue balls?

The student should state that there are x blue balls. From this, they may determine that overall, the number of blue and green balls combined must be 4x, and hence the number of red balls is therefore '100-4x'. We know this is equal to 16, so using some simple rearranging, we get that x=21. (100-4x = 164x = 84x=21) We can then find the number of each of the blue, red and green balls respectively by simple multiplication, giving us 21, 16, and 63 respectively. (A simple addition at this point could reassure the student that the calculations work, since 16+21+63 = 100). Then, simply, the ratios of red to green are 16:63, and red to blue is 16:21.