SOLUTION: Sue has two more nickels than dimes and three more quarters than nickels. She has $3.35 in all. How many coins of each kind does she have?

Question 131957: Sue has two more nickels than dimes and three more quarters than nickels. She has $3.35 in all. How many coins of each kind does she have?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Number of nickels: n
Number of dimes: d
Number of quarters: q

Given:
, two more nickels than dimes,
, three more quarters than nickels

Value of n nickels is cents
Value of d dimes is cents
Value of q quarters is cents

Total money is $3.35 which can also be expressed as 335 cents.

Since and , by substitution we can say that

Now take the value equation and substitute the two expressions for nickels and quarters in terms of dimes in place of the n and q variables:

Distribute and collect terms:

Add -135 to both sides:

Divide by 40:

So there are 5 dimes. That means there are nickels and quarters.

Check the answer:
10 quarters is $2.50,
5 dimes is $.50,
7 nickels is $.35, and finally,
$2.50 plus $.50 plus $.35 = $3.35.

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