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

Question 122344: 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?
How do we set this up? How do we solve for two unknown variables when all we have is a value?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!



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

RELATED QUESTIONS
While cleaning out the closet, john found a box of coins. The box contained nickels,... (answered by checkley71)

Sam found a number of nickels, dimes, and quarters in his room. He found 6 more dimes... (answered by jim_thompson5910)

Mr. Coleman our principal decided to redesign his rectangular rose bed into the shape of... (answered by venugopalramana)

Sam found a number of nickels,dimes, and quarters in his room. He found three more dimes... (answered by josmiceli,Edwin McCravy)

Sam found a number of nickels, dimes, and quarters in his room. He found three more dimes (answered by scott8148)

Sam found a number of nickels, dimes, and quarters in his room. He found three more... (answered by solver91311,ankor@dixie-net.com)

Sam found a number of nickels, dimes and quarters in his room. He found 3 more dimes than (answered by nerdybill)

Sam found a number of nickels, dimes and quarters in his room. He found 3 more dimes than (answered by gonzo)

Sam found a number of nickels, dimes, and quarters in his room. He found 6 more dimes... (answered by jim_thompson5910,josmiceli)