SOLUTION: Mr. Sheehan was cleaning his room when he discovered a bunch of coins under the bed. He found 20 nickles and dimes totaling $2.60. How man of each kind did Mr. Sheehan find? H

You have more than just a value.  You have a total number of coins as well.


Let n be the number of nickels, and d be the number of dimes.  First thing
we know is that .  We'll call this the quantity equation


We also know that the value of one nickel is 5 cents, so the value of n
nickels must be 5n cents.  Similarly, the value of d dimes is 10d cents.


The total value of the coins is $2.60, which can be expressed as 260 cents, so:


, and we'll call this the value equation.


Looking at the quantity equation, we can solve it for n: .


Substitute this expression for n in the value equation:





And then solve the single equation in the single variable.  The problem here is
that you have an impossible situation.  If you only have nickels and dimes
totaling 20 coins, the largest amount of money you could have would be $2.00
(if you had 20 dimes and zero nickels).  So the given total value of $2.60 is
absurd.  I'm thinking that you perhaps made a typing error, either you have 30
coins, or their value is only $1.60.

Assuming the former:




 => 
 and 


Assuming the latter:



 => 
 and