Scott has 92 coins consisting of quarters and Nickles in his pocket with a total value of $20.Solve this by using elimination

Question

Solve it my elimination

Answer 1

Let:

    N = number of Nickels

    Q = number of quarters

 

"Scott has 92 coin"     means

    N + Q = 92             [eq1]

 

 

"total value of $20"             means

     value in nickels        +       value in quarters      = 2000             [let's use cents]

        5N                       +            25Q                   = 2000       [eq2]

 

To use elimination, we make the coefficient of one of the variables the same (or opposite) so we can subtract (or add) equations to eliminate that variable:

 

        5N    +     25Q       =     2000                 [eq2]

        5N    +       5Q       =       460                 [from [eq1]]

   ---------------------------------------         [elimination; subtract equations]

                       20Q       =      1540                 [eq3]

                           Q = 77

             There are 77 quarters   (worth $19.25)

 

Now, quite often, teachers and books use substitution to find N, but let's use elimination:

               N   +    Q   =  92

                           Q   =  77

  --------------------------------      [elimination; subtract equations]

                N              =  15

             There are 15 nickels   (worth $0.75)

 

Check: $19.25 + $0.75 = $20.00

Answer 2

Let x = the number of quarters Scott has

Let y = the number of nickels Scott has

x + y = 92                   Multiply this equation by -5 and add to the last equation.

.25x + .05y = 20        Multiply this equation by 100 to get rid of the decimal points.

25x + 5y = 2000

  -5x - 5y = -460

         20x = 1540

             x = 77 quarters

77 + y = 92

y = 15 nickels