150 is 40% of what number

Question

150 is 40 percent of what number.

Answer 1

 

You can also translate from words to mathematical terms.

 

    150 is 40% of what number

 

    "is" means "="

     "of" means multiplication

     "per cent" means per 100, or divided by 100

      since we don;t know what the number is, we can use a variable "N" to represent that 

 

      150 is 40% of what number

 

      150 = 40/100 • N

 

Then reduce and solve for N

 

      150 = (2/5)N

 

Multiply both sides by the reciprocal of 2/5, which is 5/2

 

      150(5/2) = (5/2)(2/5)N

      750/2 = M

      375 = N

 

Answer 2

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Answer 3

You can also use a proportion.  You know that a percent is a number out of 100.  Also, 150 is a piece of some number.  Therefore, you will have

 

40 / 100 = 150 / x

 

 

40/100 can be reduced to 2/5.  So the new proportion is

 

2 / 5 = 150 / x

 

where x is the whole number.

 

 

Solve this proportion for x.

Answer 4

 

 

150 is 40% of what number?

 

"is" means =

 

change 40% to a decimal by moving two to the left: .40

 

"of" means multiplication

x = unknown number

 

So:

 

150 = .40 x

 

 

To solve, get x by itself. This means that whatever is going on with the x, you have to do the opposite to both sides of the equation. In this case, x is being multiplied by .40. So, you have to do the opposite: divide both sides by .40.

 

150/.40 = .40x/.40

 

This cancels the .40 out on the side with the x and leaves you with:

 

150/.40 = x

 

Now, just divide 150 by .40, and you get: 

 

375 = x

 

 

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