word problem

Question

how do I go about answering these kinds of questions?

The sum of two numbers is 20.  One number is four less than the other.  Find the numbers.

Answer 1

It's that pesky 'x' again, you have to figure out what equals.

 

Looking at the problem, you know that there are two numbers, so there are 2 values you have to come up with, and that together they add up to 20. Do you know anything else about the two numbers? Yes -- one of them is 4 less than the other. So if we call the 1st one x and the other is four less, we can call it x - 4.

 

Add them together:  x + (x - 4) = 20

 

Now we have a balance equation and a place to start figuring out what x is. To do this, we must isolate the X on one side. First, combine like kinds on the left side (we can drop the parenthesis).

 

2x - 4 = 20

 

Next, lets get rid of the -4 on the left side by adding 4 to it. In a balanced equation, you can do what ever you want to the problem as long as you do the same thing to each side.

 

2x - 4 + 4 + 4

2x = 24

 

To continue to isolate the x, we will divide both sides by 2.

 

2x = 24

2        2

 

The 2's on the left side cancel out, leaving

 

x = 12

 

Going back to the original problem,

 

x + (x - 4) = 20

 

12 + (12 -4) = 20

12 + 8 = 20

 

Our two numbers are 12 and 8