John has 30 marbles, 18 of which are red and 12 of which are blue. Jane has 20 marbles, all of them either red or blue. If the ratio of the red marbles to the blue marbles is the same for both John and Jane, then John has how many more blue marbles than Jane?
John's red ratio = 18/30
Using a GCF for (18, 30), we get 6.
Divide top and bottom of 18/30 by 6, we get 3/5
John's blue ratio is 12/30
Using a GCF of (12, 30), we get 6.
Divide top and bottom of 12/30 by 6, we get 2/5
Use these same ratios for Jane, we get:
Red: 3(20)/5 = 12
Blue: 20 - 12 = 8
Now the problem asks how many more blue marbles John has then Jane. We have 12 - 8 = 4.
John's red ratio = 18/30
Using a GCF for (18, 30), we get 6.
Divide top and bottom of 18/30 by 6, we get 3/5
John's blue ratio is 12/30
Using a GCF of (12, 30), we get 6.
Divide top and bottom of 12/30 by 6, we get 2/5
Use these same ratios for Jane, we get:
Red: 3(20)/5 = 12
Blue: 20 - 12 = 8
Now the problem asks how many more blue marbles John has then Jane. We have 12 - 8 = 4.