you have 37 coins that are nickels, dimes, and pennies. The total value of the coins is $1.55. There are twice as many pennies as dimes. Find the number of each type of coin in the bank.

Question

Solve this system by writing a matrix equation, then solve using the inverse with a calculator.

Answer 1

To solve this problem, we need to write a system of equations.

Let p = # of pennies, n= # of nickels, d= # of dimes

System of equations:

.01p +.05n + .10d = 1.55 (equation that deals with the total amount of money)

p + n + d = 37 (37 coins total)

p = 2d (twice as many pennies as dimes)

We need to convert the last equation to standard form:

p = 2d

p-2d = 0

p + 0n - 2d = 0 (remember the coefficient for nickels when writing the matrix)

Your matrix should look like:

[ .01 .05 .10 1.55 ]

[ 1 1 1 37 ]

[ 1 0 -2 0 ]

Now reduce the matrix to reduced row-echelon form:

[ 1 0 0 20 ]

[ 0 1 0 7 ]

[ 0 0 0 10 ]

20 pennies, 7 nickels, and 10 dimes are the 37 coins that total $1.55