Question: 292.5 is 65 percent of what number?

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Question: Your friend has a bag of marbles, and he tells you that 65 percent of the marbles are red. If there are 292.5 red marbles. How many marbles does he have altogether?

Answer: 450 marbles.

How To: In this problem, we know that the Percent is 65, and we are also told that the Part of the marbles is red, so we know that the Part is 292.5.

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 292.5.

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

292.5 × 100 = 29250

In step two, we take that 29250 and divide it by the "Percent", which we are told is 65.

So, 29250 divided by 65 = 450

And that means that the total number of marbles is 450.

Question: A high school marching band has 292.5 flute players, If 65 percent of the band members play the flute, then how many members are in the band?

Answer: There are 450 members in the band.

How To: The smaller "Part" in this problem is 292.5 since there are 292.5 flute players and we are told that they make up 65 percent of the band, so the "Percent" is 65.

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.

292.5 × 100 = 29250

For step two, we divide that 29250 by the "Percent", which is 65.

29250 divided by 65 equals 450

That means that the total number of band members is 450.

Another step by step method

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

Step 2: First writing it as: 100% / Y = 65% / 292.5

Step 3: Drop the percentage marks to simplify your calculations: 100 / Y = 65 / 292.5

Step 4: Multiply both sides by Y to move Y on the right side of the equation: 100 = ( 65 / 292.5 ) Y

Step 5: Simplifying the right side, we get: 100 = 65 Y

Step 6: Dividing both sides of the equation by 65, we will arrive at 450 = Y

This leaves us with our final answer: 292.5 is 65 percent of 450

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