Question: 112 is 20 percent of what number?

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Sample questions, answers, and how to

Question: Your friend has a bag of marbles, and he tells you that 20 percent of the marbles are red. If there are 112 red marbles. How many marbles does he have altogether?

Answer: 560 marbles.

How To: In this problem, we know that the Percent is 20, and we are also told that the Part of the marbles is red, so we know that the Part is 112.

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 112.

So step one is to just multiply that Part by 100.

112 × 100 = 11200

In step two, we take that 11200 and divide it by the "Percent", which we are told is 20.

So, 11200 divided by 20 = 560

And that means that the total number of marbles is 560.

Question: A high school marching band has 112 flute players, If 20 percent of the band members play the flute, then how many members are in the band?

Answer: There are 560 members in the band.

How To: The smaller "Part" in this problem is 112 since there are 112 flute players and we are told that they make up 20 percent of the band, so the "Percent" is 20.

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.

112 × 100 = 11200

For step two, we divide that 11200 by the "Percent", which is 20.

11200 divided by 20 equals 560

That means that the total number of band members is 560.

Another step by step method

Step 1: Let's assume the unknown value is Y

Step 2: First writing it as: 100% / Y = 20% / 112

Step 3: Drop the percentage marks to simplify your calculations: 100 / Y = 20 / 112

Step 4: Multiply both sides by Y to move Y on the right side of the equation: 100 = ( 20 / 112 ) Y

Step 5: Simplifying the right side, we get: 100 = 20 Y

Step 6: Dividing both sides of the equation by 20, we will arrive at 560 = Y

This leaves us with our final answer: 112 is 20 percent of 560

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