the sum of 2 numbers is 136.

Question

If four times the smaller number is subtracted from the larger number , the resut is 16. Find the 2 numbers

Answer 1

We assign variables for the numbers we want to find.

 

Let x = the smaller number

Let y = the larger number

 

 

The first part says the sum of the two numbers is 136.  Write an equation for represents this.

 

x + y = 136

 

 

Now we translate the second part, the subtraction part.

 

y - 4x = 16          or          -4x + y = 16

 

 

We have two equations to work with.

 

   x + y = 136              eq1

-4x + y =  16                eq2

 

 

We have two equations with each one having two unlike variables.  We can use the elimination method to eliminate one of the variables and obtain one equation.

 

We can subtract eq2 from eq1 to eliminate the y terms, since the variable y in both equations have a coefficient of 1.

 

5x = 120

  x = 24

 

 

Substitute this value of x into eq1 to solve for y.

 

y = 136 - x

y = 136 - 24

y = 112

 

The two numbers are 24 and 112.