Sample questions, answers, and how to
Question: Your friend has a bag of marbles, and he tells you that 75 percent of the marbles are red. If there are 75 red marbles. How many marbles does he have altogether?
Answer: 100 marbles.
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How To: In this problem, we know that the Percent is 75, and we are also told that the Part of the marbles is red, so we know that the Part is 75.
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 75.
So step one is to just multiply that Part by 100.
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75 × 100 = 7500
In step two, we take that 7500 and divide it by the “Percent”, which we are told is 75.
So, 7500 divided by 75 = 100
And that means that the total number of marbles is 100.
Question: A high school marching band has 75 flute players, If 75 percent of the band members play the flute, then how many members are in the band?
Answer: There are 100 members in the band.
How To: The smaller “Part” in this problem is 75 since there are 75 flute players and we are told that they make up 75 percent of the band, so the “Percent” is 75.
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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75 × 100 = 7500
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For step two, we divide that 7500 by the “Percent”, which is 75.
7500 divided by 75 equals 100
That means that the total number of band members is 100.
Another step by step method
Step 1: Let’s assume the unknown value is Y
Step 2: First writing it as: 100% / Y = 75% / 75
Step 3: Drop the percentage marks to simplify your calculations: 100 / Y = 75 / 75
Step 4: Multiply both sides by Y to move Y on the right side of the equation: 100 = ( 75 / 75 ) Y
Step 5: Simplifying the right side, we get: 100 = 75 Y
Step 6: Dividing both sides of the equation by 75, we will arrive at 100 = Y
This leaves us with our final answer: 75 is 75 percent of 100
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