twice as many dimes as nickels equals $1.00

Question

Elliot has nickels and dimes in his pocket.  He has twice as many dimes as nickels.  If the total value of the coins in his pocket is $1.00, how many of each coin does he have?

Answer 1

assign variables to each kind of coin:

     n = # of nickels 

     d = # of dimes

A nickel has a value of $0.05 and a dime has a value of $0.10

Since the total value of the coins is $1.00, then 

   (value of nickel * # of nickels) + (value of dime * # of dimes) = 1.00

   (0.05 * n) + (0.10 * d) = 1.00

   0.05n + 0.10d = 1.00

Since there are twice as many dimes as nickels, then the # of dimes is equal to two times the # of nickels. That is,   d = 2n.

Substitute 2n for d in the equation above:

     0.05n + 0.10(2n) = 1.00

     0.05n + 0.20n = 1.00

Combine like term:

     0.25n = 1.00

Divide both sides of the equation by 0.25 to solve for n:

     0.25n/0.25 = 1.00/0.25

     n = 4

Since we found that the # of dimes equals two times the # of nickels, then we solve for d as follows:

     d = 2n

     d = 2(4)

     d = 8

Therefore, we have 4 nickels and 8 dimes.

We can check the answer by finding the total amount of each kind of coin we have them adding the two values up:

     4 nickels worth $0.05 per nickel:   (0.05)(4) = 0.20   ==>     $0.20

     8 dimes worth $0.10 per dime:   (0.10)(8) = 0.80   ==>     $0.80

     $0.20 + $0.80 = $1.00