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 penniesx 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.

I have:

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