the larger of two numbers is 5 less than three times the smaller number. the sum of the two numbers is 47. find the two numbers

Question

I need help on this math problem. I know its probably super easy but still.

Answer 1

Let x and y be the two numbers.

  "the larger of two numbers is 5 less than three times the smaller number"  means

                  x                      =   -5      +        3    *                    y              (eq1)

 

  "the sum of the two numbers is 47"  means

                 x  +  y                   =   47               (eq2)

 

Now, the easy math (let's use elimination method):

       x   -    3y      =    -5                    (from eq1)

       x   +    y       =   47                    (eq2)

  ---------------------------    (elimination; subtract equations)

             -4y         = -52

               y         = 13         (divide both sides by -4)

      x   +  y         = 47

  --------------------------   (elimination; subtract equations)

     -x                 = -34

       x                = 34      (multiply both sides by -1)

 

Checking (very important):

  Is  34 = -5 +3*13   ?

       34 = -5 + 39   ?

       34 =  34   ? yes

  Is  34 + 13 = 47   ?

          47 = 47   ? yes