Two numbers total 51 and have a difference of 7. Find the two numbers

Let the bigger number  =  a

And the smaller number  =  b

 

We know that

a + b  =  51

 

And we know that

a - b  =  7

 

Since we know that

a - b  =  7          , we can add  b  to both sides of the equation to conclude that

a  =  7 + b

 

Again, we know that

a + b  =  51          Now that we know  a  is equal to  7 + b ,  we can substitute  7 + b  in for  a

(7 + b) + b  =  51          And now we can solve this equation for  b

7 + b + b  =  51          One apple plus one apple equals two apples, so one b plus one b equals two b's

7 + 2b  =  51          Subtract  7  from both sides of the equation.

2b  =  44          Divide both sides by  2

b  =  22

 

And again, we know that

a  =  7 + b          Now that we know  b  is equal to  22 ,  we can substitute  22  in for  b

a  =  7 + 22

a  =  29

 

To recap:

a  =  29

b  =  22