Question

A sack contains yellow marbles and black marbles. If one marble is drawn at random, the probability that it is yellow is 7/8. Six yellow marbles are added to the sack. Now, if one marble is drawn, the probability that it is yellow is 9/10. How many yellow and black marbles were initially in the sack?

Answer 1

original bag
yellow marbles -- y
black marbles --b

so y/(y+b) = 7/8
8y = 7y + 7b
y = 7b

new bag:
yellow marbles -- y+6
black marbles --- b

(y+6)/(y+6+b) = 9/10
10y+60 = 9y+54+9b
y = 9b - 6

then 9b-6 = 7b
2b=6
b = 3
then y = 7(3) or 21

so there were 21 yellow and 3 black
for a total of 24 marbles

check:
Prob(yellow) = 21/24 = 7/8

new bag:
27 yellow, still 3 black, total 30
prob(yellow) = 27/30 = 9/10

Answer 2

how did you get a positive 6

Answer 3

In your question, didn't it say that 6 yellow marbles were added ????