Question

Bobby places 12 cards on a table. Each card is either red or black in
colour. If the fraction of black cards is
7/12, What is the smallest number of
additional cards that Bobby needs to put on the table so that the fraction
of black cards becomes 5/8?

Answer 1

Note that the subject is not Ps help. You should put math so a math prof will know to help.

Answer 2

If he adds x black cards and y red cards, we need
(7+x)/(12+x+y) = 5/8
3x = 5y+4
The smallest integer solution to that is x=3, y=1
check:
(7+3)/(12+4) = 10/16 = 5/8