Two numbers have a sum of 303 and a difference of 63. Find both numbers

Question

 Please help me find the answer to this problem.

Answer 1

Hi Bekka, 

Step One: Let Statements

Let x= one of the numbers 

Let 303-x= the other number 

Step Two: Create an equation

(303-x)-x=63 

303-x-x=63 Combine like terms

303-2x=63 Rearrange

303-63=2x Simplify

240=2x Divide both sides by 2

120=x

∴The numbers are 120 and 183.

Sincerely, 

Starlyte H.

Answer 2

Hi Bekka,

 

This is a system of equations. We want to use two variables.

 

We know that our numbers add to give 303, so

x + y = 303

 

We also know that our numbers subtract to give 63, so 

x - y = 63

 

We can add these two equations together and get

x + y + x - y = 303 + 63    Combining like terms gives

2x = 366

x = 183

 

Now we can substitute in the value of x into one of the original equations (it doesn't matter which one you pick)

x + y = 303

183 + y = 303

y = 120

 

Feel free to write back here if you have more questions.