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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”

Respuesta :

frika

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.

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