The ratio of the number of beads karen had to the number of beads patricia had was 2: 5. after karen bought another 75 beats the ratio became 4: 15. how many beads did each girl have at first?

White shapes and black shapes are used in a game. some of the shapes are circles. while the rest are squares. the ratio of the number of white shapes to the number of black shapes is 5: 11. the ratio of the number of white cicrles to the number of white squares is 3: 7. the ratio of the number of black circles to the number of black squres is 3: 8. work out what fraction of all the shapes are circles.