The number 297 is 24 3/4 % of which the following?

Question

^{Ans is 1200, but how?}

 

Thanks

Answer 1

Let x = the number

 

Translate:

  "297 is 24 3/4 % of x"

    297 = 24 3/4% * x     ["is" means equals; "of" means multiply]

 

Now, percents are parts of 100, so, for example, 5% = 5/100 = 0.05.  You may use the one that best fits the problem.

 

Since 24 3/4 % is 0.2475, you may like that.  But, if you want a fraction rather than a decimal, the 24 3/4% becomes 99/400 as an improper fraction.

 

Let's solve both ways:

    297 = 0.2475*x

     297 / 0.2475 = x      [divide both sides by 0.2475]

     1200 = x

or

    297 = (99/400)x

    297*(400/99) = x      [multiply both sides by 400/99, which is dividing by 99/400]

    1200 = x

Answer 2

Mandip,

 

I assume you mean that 297 is 24 and 3/4% of some number, and you want to find that number.  I suggest setting the problem up as a proportion:

 

297 → 24.75

x → 100

 

x = 297*100/24.75 = 1200

Answer 3

I am assuming the question reads 297 is 24 and 3/4ths percent of what number.

To answer a question like this, you need to know certain things. First, you know 297 is a fraction of some number since the problem states that is a percentage of some number. You also know that percentage is 24 and 3/4ths percent, ie. 24.75% (simple fraction to decimal conversion). 24.75% can also be written as 24.75/100. Thus, we now have two fractions which equal each other. This is written out below:

297/x = 24.75/100



From there, we solve for x. There is a simple way to solve these types of fractional equations. Basically, you multiply diagonally. Ie. multiply the numerator on the left with the denominator on the right and vice versa.
Your equation is gonna look like this now:

24.75x = 29700

To solve for x, simply divide both sides by 24.75.
Now your equation looks like this:

x = 1200.

If you'll remember, we established x as the number we were solving for in the initial question. Thus your answer is 1200!

Hope this helps.