The sum of two numbers is 70. The larger number is 4 more than twice the smaller number. What is the smaller number?

Question

I have been struggling with word problems and I never could get the hang of them. Please answer! I'm done trying to get it by myself.

Answer 1

Let x and y be the two unknown numbers.

• The sum of two numbers is 70:  x + y = 70
• The larger number (y) is 4 more than twice the smaller number (x):  y = 2x + 4

 

Since x + y = 70, y = 70 -x.  Substitute 70-x in place of y in the second equation:

 

      y = 2x + 4

      70 - x = 2x + 4

      70 = 3x + 4

      66  = 3x

     

     22 = x  (This is the smaller number)

 

The larger number is y = 70 - x = 70 - 22 = 48