larger number/smaller number

Question

The sum of two numbers is 66. If twice the smaller number is subtracted from the larger? number, the result is 15. Find the two numbers.

Answer 1

Jessica,

 

Let x be the first number and y the second.

 

Then:

 

x + y = 66 (1)

 

Also, subtracting 2 times the smaller from the larger gives 15.  We can write this as:

 

y - 2x = 15  (2) (assuming x is the smaller of the two)

 

Now, we can use elimination to solve for y by subtracting eq2 from eq1:

 

  x + y = 66

-

-2x + y = 15 (rearranged eq2)

 

=>

 

3x = 51 (the y's go away)

 

=>

 

x = 17

 

To find y, substitute 17 in for x in eq1

 

17 + y = 66

 

y = 66 -17 = 49