+231 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 7:3. How many blue marbles were in the bag before I added more?
Grant you mercy if 't be true thee solveth this
+129852 Let the number of original yellow marbles = Y
Let the number of original blue marbles be = B
And we know that B/Y = 4/3 ⇒ B = (4/3)Y ⇒ Y = (3/4)B
And we have that
B + 5 7
_____ = ___
Y - 3 3
Subbing for Y we have that
B + 5 7
_________ = ___ cross-multiply
(3/4)B - 3 3
3(B + 5) = 7 [ (3/4)B - 3 ] simplify
3B + 15 = (21/4)B - 21 add 21 to both sidws, subtract 3B from both sides
36 = (21/4 - 3)B
36 = ( 21/4 - 12/4) B
36 = (9/4)B multiply both sides by 4/9
16 = B = original number of blue marbles
