how many of each coin does he have?

Question

jon throws all his nickels and dimes in a jar at home each day. he counted all his coins one day and found that he had collected $42.35. If there were five times as many nickels as dimes, how many of each coin does he have?

 

Answer 1

First you set up the equation for the amount of money he has, knowing that nickels cost $0.05 and dimes cost $0.10:

 

0.10d + 0.05n = 42.35

 

where n is the amount of nickels and d is the amount of dimes.

 

Next you set up an equation for the relative amount of coins. Because we know that he has five times as many nickels as he does dimes, the amount of nickels he has is 5 times greater than the amount of dimes:

 

n = 5d

 

and we have to switch up this above equation so it looks like this:

 

5d - n = 0

 

Now we have two equations with the same variables. We can combine the equations to eliminate one variable, but first we have to set it up so that one variable in one equation can cancel out the same variable in the other, like this:

 

take the equation at the top and multiply all of the terms by 20:

 

[0.10d + 0.05n = 42.35]20

2d + n = 847

 

Then take the second equation and add it from this new equation like this:

 

             2d + n = 847

         +[ 5d - n = 0  ]

 ___________________

             7d + 0 = 847

 

So now we have eliminated one variable, leaving us with only d to work with. Now we just solve for d from this new equation:

 

7d = 847

d = 121

 

So he has 121 dimes. We know that he has five times as many nickels as dimes, so he has 121 x 5 = 605 nickels. And if you would like to check your work, you can plug in the amount of nickels and dimes into the very first equation:

 

$0.05(605) + $0.10(121) = $42.35