SOLUTION: Your brother and sister have a jar containing 80 coins, all which are either quarters or nickels. The total value of the coins is &14.60. How many of each type of coin do they ha

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Question 1102797: Your brother and sister have a jar containing 80 coins, all which are either quarters or nickels. The total value of the coins is &14.60.
How many of each type of coin do they have?
SO far I have,
q=quarters
n=nickels
q+n=80
q+n=14.60

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52832)   (Show Source):
You can put this solution on YOUR website!
.

n + q = 80 (1) (counting coins) 5n + 25q = 1460 (2) (counting value in cents) From eq(1) express n = 80-q and substitute it into equation (2). You will get 5*(80-q) + 25q = 1460, ====> 400 - 5q + 25q = 1460 20q = 1460 - 400 ====> 20q = 1060 ====> q = = 53. Answer. 53 quarters and 80-53 = 27 nickels.

Solved.

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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
    - Three methods for solving standard (typical) coin word problems
    - 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.

You will find there the lessons for all levels - from introductory to advanced,
and for all methods used - from one equation to two equations and even without equations.

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".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!

Let me specifically address the work you show you did to try to set up the problem. There is one thing you can do that will make it easier for you to see how to set up the problem correctly.

Your start to the problem was this:

q=quarters
n=nickels
q+n=80
q+n=14.60

Note that, algebraically, those last two equations don't make sense. If q+n is 80, how can it also be 14.60?

Your trouble is that you have written your equations without a clear understanding of what q and n represent. And you don't have a clear understanding of what q and n represent because you didn't define them clearly enough.

Clearly what you mean is this:
q = the number of quarters
x = the number of nickels

With those definitions, it is clear that "q+n=80" is true, because the total number of coins is 80.

But now "q+n=14.60" does NOT make sense, because "14.60" is not the total number of coins.

What IS the "14.60"? It is the total VALUE (in dollars) of the coins.

Since each quarter is worth .25 dollars and each nickel is worth .05 dollars, the equation using the "14.60" given in the statement of the problem needs to say the total VALUE of the quarters, plus the total VALUE of the nickels, is $14.60:

.25q + .05n = 14.60

TAKE THE TIME to write out CLEAR and PRECISE definitions of the variables and expressions you are going to us, and setting up problems correctly will be much easier.