Question: 71.2 is 40 percent of what number?

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Question: Your friend has a bag of marbles, and he tells you that 40 percent of the marbles are red. If there are 71.2 red marbles. How many marbles does he have altogether?

Answer: 178 marbles.

How To: In this problem, we know that the Percent is 40, and we are also told that the Part of the marbles is red, so we know that the Part is 71.2.

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 71.2.

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

71.2 × 100 = 7120

In step two, we take that 7120 and divide it by the "Percent", which we are told is 40.

So, 7120 divided by 40 = 178

And that means that the total number of marbles is 178.

Question: A high school marching band has 71.2 flute players, If 40 percent of the band members play the flute, then how many members are in the band?

Answer: There are 178 members in the band.

How To: The smaller "Part" in this problem is 71.2 since there are 71.2 flute players and we are told that they make up 40 percent of the band, so the "Percent" is 40.

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.

71.2 × 100 = 7120

For step two, we divide that 7120 by the "Percent", which is 40.

7120 divided by 40 equals 178

That means that the total number of band members is 178.

Another step by step method

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

Step 2: First writing it as: 100% / Y = 40% / 71.2

Step 3: Drop the percentage marks to simplify your calculations: 100 / Y = 40 / 71.2

Step 4: Multiply both sides by Y to move Y on the right side of the equation: 100 = ( 40 / 71.2 ) Y

Step 5: Simplifying the right side, we get: 100 = 40 Y

Step 6: Dividing both sides of the equation by 40, we will arrive at 178 = Y

This leaves us with our final answer: 71.2 is 40 percent of 178

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