Ms.Lynch has 21 coins in nickels and dimes. Their total value is $1.65. How many of each coin does she have?

Question

Ms.Lynch has 21 coins in nickels and dimes. Their total value is $1.65. How many of each coin does she have?

Answer 1

Hi Loopy,

 

There are several ways to get at the answer.  I'm going to show you the combination method for systems of equations.

 

Let's use x for nickles and y for dimes.  To avoid decimal numbers, I'll use numbers in terms of cents, not dollars.

 

So we know x + y = 21 and 5x +10y = 165

 

We line them up in columns

    x +   y =   21

  5x +10y = 165

 

To eliminate the x variable, I'll multiply every element in the 1st equation by -5.

 -5x + -5y = -105
  5x + 10y =  165

 

Now we combine (add) the equations, which eliminates x altogether.

  5y = 60   ...   y = 12

 

From there, x + 12 = 21  ...  x = 21-12  ...  x = 9

 

You should double check.  Do 9 nickles and 12 dimes equal $1.65?

 

A very important thing to remember using this method is to do the same thing to each element in the equation that you change!

 

I hope that helps.

 

Paul L.