Mark has a bag that contains exactly 3 black marbles, 6 gold marbles, 2 purple marbles and 6 red

In order to determine the probability that a marble drawn from the bag is black or gold, we divide the number of black and gold marbles in the bag by the total number of marbles in the bag. In other words,

Probability of selecting a black or gold marble = Number of black or gold marbles/ Total number of marbles

When Mark adds white marbles to the bag, this does not change the number of black or gold marbles. Therefore, the number of black or gold marbles in the bag is 3 + 6 = 9. We are also given that the probability of drawing a black or gold marble is 3/7 So the equation

Probability of selecting a black or gold marble =Number of black or gold marbles/ Total number of marbles
becomes

3/7=9/Total number of marbles

Since 3/7=9/21, this tells us

9/21=9/ Total number of marbles

Therefore, the total number of marbles is 21.

Originally, there were 3 + 6 + 2 + 6 = 17 marbles in the bag. Then Mark added some white marbles. Since the total number of marbles in the bag after adding some white marbles is 21, Mark must have added 21 − 17 = 4 white marbles.