The sum of two numbers is 18 and their diffrence is 4 what is the answer?

Answer 1

Let's use some algebra to solve this problem! Lets call our two numbers we need to find X and Y.

The question gives us two pieces of information.

X + Y = 18

X - Y = 4

Now we are going to add the two equations together. We just add directly down the columns.

X + Y = 18

+ X - Y = 4

_______________

2X + 0 = 22

so 2X= 22.

Now divide both sides by two to get: X = 11

Now that we have the value of X we can plug the value into either of the original equations to find Y.

X + Y = 18

11 + Y = 18

Subtract 11 from both sides to get:

Y = 7

So now we know our two mystery numbers are 11 and 7! Done

Another Approach

If that was a little hard to understand, we can use just addition and subtraction to get our answer. Just remember Algebra works for all numbers, even really big numbers. The below approach only works for small numbers, but it's great addition and subtraction practice.

We are going to make a table of all the (positive) numbers that add up to 18 until we find two numbers that also have a difference of 4. Do not try this for numbers bigger than 20, or it will take way too much time.

1 + 17 = 18 17-1= 16

2 + 16 = 18 16-2 =14

3 + 15 = 18 15-3= 12

4 + 14 = 18 14-4=10

PS. If you are noticing a pattern above, go ahead and make a rule for your pattern that you can apply to find your answers.

Eventually you will get:

7 + 11 = 18 11 - 7 = 4

The answer is 11 and 7

Answer 2

Hi, Kathryn!

X + (x + 4) = 18

x + x + 4 =18

2x - 4 = 18

2x + 4 - 4 = 18 - 4

2x = 14

2x/2 = 14/2

x = 7

X + 4 = 7 + 4 = 11

11 + 7 = 18