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a collection of coins consist of nickels, dimes, and quarters. there are 3 fewer quarters than nickels and six more dimes than quarters. how many of each kind of coin is in the collection if the total value of the collection is $4.35?

Respuesta :

There are 12 Nickels, 9 Quarters, and 15 Dimes.
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Using a system of equations, there are 9, 12 and 15 quarters, nickels and dimes respectively.

Creating a system of equations thus :

  • n + d + q = 36 - - - (1)
  • n = q + 3 - - - (2).
  • d = q + 6 - - - (3)

Substitute for n and q

(q+3) + (q+6) + q = 36

3q + 9 = 36

3q = 36 - 9

q = 27 ÷ 3

q = 9 quarters

n = 9 + 3 = 12 nickels

d = 9 + 6 = 15 dimes

Hence, there are 9, 12 and 15 quarters, nickels and dimes respectively.

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