How many nickels are in the jar

Question

A drawer contains quarters and nickels. There are 200 total coins valuing $30.00. Think about a system of equations that can be used to represent the number of quarters and nickels and then think it through using substitution to solve the system of equations. How many nickels are in the jar

Answer 1

Justin,

Mark gave you a correct setup for this problem (one line below).  See also my comment.

Answer 2

q represents the number of quarters

n represents the number of nickels

 

q + n = 200

0.25q + 0.05n = 30.00

 

Now you can solve for n.

Answer 3

There are two variables -- the number of quarters and the number of nickels.

 

   Let Q=number of quarters

        N=number of nickels

        

The value (in cents) of Q quarters is 25Q.  The value (in cents) of N nickels is 5N.

 

"valuing $30.00"     means    25Q + 5N = 3000       [in cents, remember?]

 

"There are 200 total coins"    means  Q + N = 200

 

To substitute, we must first use one equation to find the value of one variable in terms of the other variable so we can substitute that into the other equation.

   Let's use:    Q = 200-N

    and    25(200-N) + 5N = 3000

 

     5000 - 25N + 5N = 3000

       2000 = 20N       [add 20N and subtract 3000 from both sides]

        100 = N

 

Then, put that into either equation to solve for Q:

      Q + (100) = 200

      Q = 100             [subtract 100 from both sides]

 

Check:

  Is 25(100) + 5(100) = 3000   ?

      2500 + 500 = 3000   ?

         3000 = 3000   ?yes

  Is 100 + 100 = 200   ?

          200 = 200   ?yes