I am having problems comprehending word problems , can you help?

Question

One number is 25% of another. The larger number is 12 more than the smaller. What are the numbers?

Answer 1

Hi Monica,

 

let's breakdown the question in parts.

 

1) One number is 25% of another.

 

Let one number be x. If this number is 25% of another, it means that the other number is 4 times this number, i.e., 4x.

 

2) The larger number is 12 more than the smaller.

We found above that the larger number is 4x and the smaller number is x.

x + 12 = 4x

3x = 12

x = 4 this is the smaller number.

4 + 12 = 16 this is the larger number. 

 

4 is indeed 25% of 16. So, our answer is correct.

 

Hope this helps!

Answer 2

First, assign symbols to the unknown quantities.  So here, 

Let L = larger number

Let S = smaller number

 

Next, take what the words tell you, and put them into equation form using these symbols.  Thus...

The larger number (L) is 12 more than the smaller number (S).  This can be written as L = S + 12

Also, it tells you that one number is 25% of the other.  Since it is 25% of something, it must be smaller, so this can be written as S = 0.25L (note that 25% is written as a decimal of 0,25)

 

You now have 2 equations with 2 unknowns:

(1)  L = S + 12

(2)  S = 0.25 L

Solve for one, and substitute in the other

Substituting (2) in (1) you have L = 0.25L + 12 and solving that you have...

L - 0.25L = 12

0.75L = 12 

L = 16

Plugging this back into equation (2):

S = 0.25L

S = 0.25 x 16

S = 4

So, the larger number is 16 and the smaller number is 4

Check this:

25% of 16 = 0.25 x 16 = 4 √

16 is 12 more than 4 √