Sample questions, answers, and how to
Question: Your friend has a bag of marbles, and he tells you that 30 percent of the marbles are red. If there are 36 red marbles. How many marbles does he have altogether?
Answer: 120 marbles.
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How To: In this problem, we know that the Percent is 30, and we are also told that the Part of the marbles is red, so we know that the Part is 36.
So, that means that it must be the Total that’s missing. Here is the way to figure out what the Total is:
Part/Total = Percent/100
By using a simple algebra we can re-arrange our Percent equation like this:
Part × 100/Percent = Total
If we take the “Part” and multiply it by 100, and then we divide that by the “Percent”, we will get the “Total”.
Let’s try it out on our problem about the marbles, that’s very simple and it’s just two steps! We know that the “Part” (red marbles) is 36.
So step one is to just multiply that Part by 100.
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36 × 100 = 3600
In step two, we take that 3600 and divide it by the “Percent”, which we are told is 30.
So, 3600 divided by 30 = 120
And that means that the total number of marbles is 120.
Question: A high school marching band has 36 flute players, If 30 percent of the band members play the flute, then how many members are in the band?
Answer: There are 120 members in the band.
How To: The smaller “Part” in this problem is 36 since there are 36 flute players and we are told that they make up 30 percent of the band, so the “Percent” is 30.
Again, it’s the “Total” that’s missing here, and to find it, we just need to follow our 2 step procedure as the previous problem.
For step one, we multiply the “Part” by 100.
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36 × 100 = 3600
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For step two, we divide that 3600 by the “Percent”, which is 30.
3600 divided by 30 equals 120
That means that the total number of band members is 120.
Another step by step method
Step 1: Let’s assume the unknown value is Y
Step 2: First writing it as: 100% / Y = 30% / 36
Step 3: Drop the percentage marks to simplify your calculations: 100 / Y = 30 / 36
Step 4: Multiply both sides by Y to move Y on the right side of the equation: 100 = ( 30 / 36 ) Y
Step 5: Simplifying the right side, we get: 100 = 30 Y
Step 6: Dividing both sides of the equation by 30, we will arrive at 120 = Y
This leaves us with our final answer: 36 is 30 percent of 120
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