SOLUTION: th problem asks a shop owner has a bag containing 15 red marbles and 1 orange marble if the owner wants to make sure the probability of choosing an orange marble is 2/5 how many or

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Question 452509: th problem asks a shop owner has a bag containing 15 red marbles and 1 orange marble if the owner wants to make sure the probability of choosing an orange marble is 2/5 how many orange marbles does she need to add?
Found 2 solutions by stanbon, bucky:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
th problem asks a shop owner has a bag containing 15 red marbles and 1 orange marble if the owner wants to make sure the probability of choosing an orange marble is 2/5 how many orange marbles does she need to add?
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Let the # she needs to add be "x":
Solve:
(1+x)/(16+x) = 2/5
5+5x = 32+2x
3x = 27
x = 9 (# of orange marbles she needs to add)
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Cheers,
Stan H.

Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
You know that the bag contains 15 red marbles.
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You are going to add a number of orange marbles to this bag. Let's call the number of orange marbles that need to be in the bag as X. When you are done adding orange marbles, the total number of marbles in the bag will the 15 red marbles plus the X orange marbles.
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The probability of drawing an orange marble from the bag will be the total number of orange marbles in the bag (X) divided by the total number of marbles in the bag (15 + X) and the problem says that this is to equal 2/5.
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So set up the probability equation as:
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and solve for X
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A quick way of getting equations of this form (that is when both sides are fractions) into a form that can be solved is to multiply the numerator on one side of the equal sign by the denominator on the other side, and do this for the terms on both sides. In other words, multiply the numerator X on the left side by the denominator 5 on the right side. Then multiply the numerator 2 on the right side by the denominator (15 + X) on the left side. Put the equal sign in between the two products to get:
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Multiply this out:
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Collect all the X terms on the left side by subtracting from both sides to get:
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Solve for X by dividing both sides by 3 and you have:
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This tells you that the bag should contain 15 red marbles and 10 orange marbles. But the bag already contains 1 orange marble. Therefore, you have to add 9 more orange marbles to have the total number of orange marbles be 10.
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A logic check of the answer tells you that you have 25 marbles in the bag, and 10 of those 25 marbles are orange while 15 are red. Therefore, if you randomly draw a marble out of the bag the chances of it being orange are:
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and by dividing both the numerator and denominator by 5, you can see that the result does reduce to:
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which says that the answer of adding 9 more orange marbles to make a total of 10 in the bag is correct.
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Hope this helps you to see how this problem is worked.