Question 1001009
Mart has $4.10 in nickels, dimes, and quarters. She has four more 
quarters than dines. She has three times as many nickels as quarters. 
How many of each coin does she have?
<pre>
Notice that I changed only the numbers in your problem.  That's because
I didn't want to do your homework for you.  All you have to do is do
yours exactly as I did this one, step by step. 
</pre>
Mart has 4.10 in nickels, dimes, and quarters. 
<pre>
  0.05N + 0.10D + 0.25Q = 4.10
</pre>
She has four more quarters than dines. 
<pre>
                      Q = D + 4
</pre>
She has three times as many nickels as quarters. 
<pre>
                      N = 3Q

So we have three equations and 3 unknowns:

  0.05N + 0.10D + 0.25Q = 4.10
                      Q = D + 4
                      N = 3Q

Multiply first equation by 100 to remove decimals

         5N + 10D + 25Q = 410
                      Q = D + 4
                      N = 3Q 

Solve the second equation for D

                      Q = D + 4
                  Q - 4 = D
                      D = Q - 4

Substitute N = 3Q and D = Q - 4 into

         5N + 10D + 25Q = 410
5(3Q) + 10(Q - 4) + 25Q = 410
   15Q + 10Q - 40 + 25Q = 410
               50Q - 40 = 410
                    50Q = 450
                      Q = 9

Substitute Q = 9 into 

                      D = Q - 4
                      D = 9 - 4
                      D = 5

Substitute Q = 9 into N = 3Q
                      N = 3(9)
                      N = 27

So Mart has 9 quarters, 5 dimes and 27 nickels.

Checking:
</pre>
Mart has $4.10 in nickels, dimes, and quarters. 
<pre>
9 quarters =  9($0.25) = $2.25
5 dimes    =  5($0.10) = $0.50
27 nickels = 27($0.05) = $1.35
------------------------------
                         $4.10

That checks:
</pre>
She has 4 more quarters than dines. 
<pre>
She has 9 quarters and 5 dimes, and 9 is 4 more than 5.

That checks.
</pre>
She has three times as many nickels as quarters. 
<pre>
She has 27 nickels and 9 quarters, and 27 is three times 9.

That checks.

Now do yours the exactly same way, step by step.

Edwin</pre>