I am choosing shapes out of a bag. The ratio of blue shapes to red shapes are 2:1. For the blue shapes, the ratio of spheres to cubes is 2:3. For the red shapes, the ratio of the spheres to cubes is 1:4. Given that there are 12 red spheres, how many blue cubes are there?
Ratio of red spheres to cubes is 1:4 which means 1 out of (1+4) are spheres 1/5 are spheres
if 1/5 x = 12 then x = 60 red pieces
Ratio of blue to red pieces 2:1 so 2/(2+1) = 2/3 are blue pieces and 1/3 are red pieces 1/3 x = 60 means x= 180 pieces all together
2/3 of these 180 pieces are blue = 120 blue pieces for blue, the ratio of spheres to cubes is 2:3 so 3/5 are cubes
3/5 * 120 = 72 blue cubes