The sum of two numbrs is 50. The first number is 43 less than twice the second number. Write and solve a system of equations to find the two numbers.

Question

PLEASE HELP

 

Answer 1

Word (story) problems help us to learn how to translate phrases into concise, precise math variables and expressions.

 

This problem says "two numbers."  Let them be x and y.

 

Translate:

  "sum of two numbrs is 50"     means   x+y=50

  "first number is 43 less than twice the second number"    means

          x          =   -43             2  *                y

 

or, rewriting,

      x = 2y-43

 

Let's substitute (replace) the value of y in the second equation with what we get from the first equation (y=50-x).

     x = 2(50-x) - 43

     x = 100 - 2x - 43                [distribute]

     3x = 57                             [add 2x to both sides; so subtraction]

       x  = 19                         [ divide both sides by 3]

 

Now, put that value of x into either equation so we can calculate the value of y  [note: which equation is easier?]

     (19) + y = 50

               y = 31

 

Checking (very important):

   Is  19 + 31 = 50   ?

           50 = 50   ? yes

  Is   19 = 2(31) - 43   ?

        19 = 62 - 43   ?

          19 = 19   ? yes

Answer 2

Make the first number x, the second number y. 

The sum of x and y is 50: x+y=50

x is 43 less than 2y: x=2y-43

replace x in equation x+y=50 with x=2y-43: 2y-43+y=50

combine like terms: 3y-43=50

add 43 to both sides: 3y=93

divide both sides by 3: y=31

replace y in equation x+y=50 with y=31: x+31=50

subtract 43 31 from both sides: x=19

 

the solution to the question is the first number is 19, the second number is 31.

Answer 3

We have a system of two equations: The numbers  x and y

 

1)   x + y = 50   and

2)   X = 2y - 43

 

by substituting  (2) in (1)

 

  2y - 43 + y = 50    simplifying

 

  3y  =  50 + 43

  3y  =  93  ..........   dividing  by  3

    y  =  31               and  replacing in (1)

    X  =  19  

 

Answer:  the nunbers are:  19 and 31