Mark has a bag that contains exactly 3 black marbles, 6 gold marbles, purple marbles and 6 red marbles. Mark finds a number of w
hite marbles and adds them to the bag. He tells Sam that if he draws a marble at random from the bag, the probability of being black or gold is 3/7. How many white marbles did Mark add into the bag?
Okie doke. So, to find out the amount of marbles in the bag so far, we can add the amounts of each color together. 3 + 6 + 2 + 6 is 17. There are 17 marbles in the bag, but we add white marbles in the bag, and the chances of getting a gold or black marble is 3/7. 3 + 6 is 9. And if know about multiples, the LCM of 3 and 7 is 21. 21 - 17 is 4. Let's set up a proportion to check this: 3/7 = x/21. Cross multiply values to get 63 = 7x. Divide each side by 7 to get 9. And that satisfies the problem. Mark added 4 white marbles in the bag.
