Question
A bag holds black, white and green marbles. If one marble is randomly chosen from the bag, the probability that it is black is 3/5. The probability that it is white is equal to the probability that it is green. If there are 9 black marbles, how many marbles are in the bag?
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Answer to a math question A bag holds black, white and green marbles. If one marble is randomly chosen from the bag, the probability that it is black is 3/5. The probability that it is white is equal to the probability that it is green. If there are 9 black marbles, how many marbles are in the bag?
Darrell
4.597 Answers
Let's assume that the total number of marbles in the bag is "x".
Given that the probability of choosing a black marble is 3/5, we can conclude that there are 3/5 of "x" black marbles in the bag.
Since the probability of choosing a white marble is equal to the probability of choosing a green marble, we can conclude that each of them is equal to 1/5 of "x".
So, the number of black marbles is 3/5 of "x", which is (3/5)x = 9.
To find the value of "x", we can solve the equation:
(3/5)x = 9
To isolate "x", we can multiply both sides of the equation by the reciprocal of 3/5, which is 5/3:
(3/5)x * (5/3) = 9 * (5/3)
x = (9 * 5) / 3
x = 15
Therefore, there are 15 marbles in the bag.
Answer: \boxed{15}.
Given that the probability of choosing a black marble is 3/5, we can conclude that there are 3/5 of "x" black marbles in the bag.
Since the probability of choosing a white marble is equal to the probability of choosing a green marble, we can conclude that each of them is equal to 1/5 of "x".
So, the number of black marbles is 3/5 of "x", which is (3/5)x = 9.
To find the value of "x", we can solve the equation:
(3/5)x = 9
To isolate "x", we can multiply both sides of the equation by the reciprocal of 3/5, which is 5/3:
(3/5)x * (5/3) = 9 * (5/3)
x = (9 * 5) / 3
x = 15
Therefore, there are 15 marbles in the bag.
Answer: \boxed{15}.
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