I have a bag with yellow and blue marbles in it. At the moment, the ratio of blue marbles to yellow marbles is 4:3. If I add 5 blue marbles and remove 3 yellow marbles, the ratio will be 13:3. How many blue marbles were in the bag before I added more?
+128407 Call the total number of marbles in the bag before we added any N
The blue ones= (4/7)N
The yellow = (3/7)N
So
[ (4/7)N + 5 ] 13
__________ = ____ cros-multiply
[ (3/7)N - 3 ] 3
3 [ (4/7)N + 5 ] = 13 [ (3/7)N - 3 ]
(12/7)N + 15 = (39/7)N - 39
(39/7)N - (12/7)N = 15 + 39
( 27/7)N = 54
N = 54 ( 7/27) = 14
The number of blue originally = (4/7)(14) = 8
