In a jar with coins, there are 10 quarters more than dimes. The amount is 12.20$. How many of each are in the jar?

Question

Plz help im stuck on In a jar with coins, there are 10 quarters more than dimes. The amount is 12.20$. How many of each are in the jar?

Answer 1

Units are important:

     (value per coin)*(number of coins) = (total value for that coin)

 

  that is:

    (value/coin)(number of coins) = (total value for that coin)

[coins cancels out]

 

Let x = number of dimes

    (x+10) = number of quarters       ["10 quarters more than dimes"]

 

Value of dime = $0.10      or    10 cents

Value of quarter = $0.25     or     25 cents

 

(total value in dimes)     +    (total value in quarters)    =    (total value of coins in jar)

        10x                      +                 25(x+10)            =    1220            [let's use cents]

 

 

  10x + 25(x+10) = 1220

  10x + 25x + 250 = 1220         [distribute]

  35x + 250 = 1220                  [collect terms]

    35x = 970

      x = 27.71428571        [Oops!!!]
    This is not possible !!

 

Check:

  FOR x = 0 TO 122         [number of dimes must be between 0 and 1220]

     y = x+10              [there are 10 more quarters than dimes]

     IF ( (10*x + 25*y) = 1220 ) THEN OUTPUT (x,y)

  NEXT x

  OUTPUT ("Done.")

 

The output:

Done.

 

There must be a typo in the problem statement.