A bag contains only red and blue marbles. Yasmine takes one marble at random from the bag. The probability that she takes a red marble is 1 in 5. Yasmine returns the marble to the bag and adds five more red marbles to the bag. The probability that she takes one red marble at random is now 1 in 3. How many red marbles were originally in the bag?
+128408 Let the original number of red marbles = R and the number of original number of blue marbles = B
And we know that
R 1
_____ = ___ cross-multiply and we have that
R + B 5
5R = R + B subtract R from both sides
4R = B (1)
And after 5 red marbles are added to the bag we have that
R + 5 1
_________ = _____ cross-multiply
R + B + 5 3
3(R +5) = R + B + 5
3R + 15 = R + B + 5 subtract R from both sides
2R + 15 = B + 5 sub (1) in for B
2R + 15 = 4R + 5 subtract 5, 2R from both sides
10 = 2R divide both sides by 2
5 = R = the original number of red marbles
