SOLUTION: A newspaper carrier has $4.60 in change. He has two more quarters than dimes but five times as many nickels as quarters. How many coins of each type does he have?

Question 1065120: A newspaper carrier has $4.60 in change. He has two more quarters than dimes but five times as many nickels as quarters. How many coins of each type does he have?
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52847)   (Show Source): You can put this solution on YOUR website!
.
A newspaper carrier has $4.60 in change. He has two more quarters than dimes but five times as many nickels as quarters.
How many coins of each type does he have?
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Let "q" be the number of quarters, "d" be the number of dimes and "n" be the number of nickels. Then what you have from the condition is d = q - 2 and n = 5q. (1) Next, you have the "value" equation 5n + 10d + 25q = 665. (2) Substitute (1) into the "value" equation. You will get a single equation for q: 5*(5q) + 10*(q-2) + 25q = 460. Simplify and solve it for q: 25q + 10q - 20 + 25q = 460, 60q = 460 + 20, 60q = 480, q = = 8. Now from (1) d = q - 2 = 8 - 2 = 6 and n = 5q = 5*8 = 40. Answer. 40 nickels, 6 dimes and 8 quarters.

There is entire bunch of lessons on coin problems
    - Coin problems
    - More Coin problems
    - Solving coin problems without using equations
    - Kevin and Randy Muise have a jar containing coins
    - Typical coin problems from the archive
    - More complicated coin problems (*)
    - Solving coin problems mentally by grouping without using equations
    - Santa Claus helps solving coin problem
    - OVERVIEW of lessons on coin word problems
in this site.

Read them and become an expert in solution of coin problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Coin problems".

Your problem is very similar to the problem 2 of the lesson marked (*) in the list.
For this response I simply copied and pasted that solution and updated the input data in it.

Answer by josgarithmetic(39625)   (Show Source): You can put this solution on YOUR website!
d dimes
n nickles
q quarters
-
and

First two equations same as

The money count equation is equivalent to .
Substituting for d and n gives an equation in q only,

Find q, and use it for evaluating d and n.
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