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?

Guest Jul 7, 2022

#1**+1 **

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

CPhill Jul 7, 2022