Uncle Hank has another riddle for his nephews he tells them,"I have the same number of nickels and pennies. I have 4 times as many quarters as nickels. I have 3 more dimes than quarters. I have a total of $6.14"

Let x be the number of nickels.

If I have the same number of nickels and pennies, then I have x pennies. If I have 4 times as many quarters as nickels, then I have 4x quaters. If I have 3 more dimes than quarters, then I have 3+4x=3+4x dimes.

Note that

penny is a one-cent coin; nickel is a five-cent coin; quater is a twenty-five-cent coin; dime is a ten-cent coin.

Then I have

x pennies x nickels = 5x pennies; 4x quaters = 4x·25=100x pennies; 3+4x dimes = (3+4x) ·10=30+40x pennies.

In total I have x+5x+100x+30+40x=146x+30 pennies that is $6.14. Since $6.14 is 614 pennies. Therefore,

146x+30=614,

146x=614-30,

146x=584,

x=584:146,

x=4.

Answer: I have:

4 pennies; 4 nickels; 4·4=16 quaters; 3+4·4=3+16=19 dimes.