Mr. Rogers has $4.62. He has 3 times as many dimes as nickels and 6 more pennies than dimes. How many coins of each kind does he have?

Let’s make x = # of nickels. Then 3x = # of dimes and 3x+6 = # of pennies. A nickel is 5 cents, a dime is 10 cents and a penny is 1 cent.

The money she has should be .05(x) + .10(3x) + .01(3x+6) = 4.62 or to make it simpler: 5(x) + 10(3x) + 1(3x+6) = 462.

5x + 30x + 3x + 6 = 462

38x + 6 = 462

38x = 456

x = 12.

So she has 12 nickels (12 * $0.05 = $0.60), 36 dimes (36 * $0.10 = $3.60) and 42 pennies (42 * $0.01 = $0.42). $3.60 + $0.60 + $0.42 = $4.62.