Question 1205955
.
You have 37 coins that are nickels, dimes, and pennies. 
The total value of the coins is $1.55. 
There are twice as many pennies as dimes. 
Find the number of each type of coin in the bank.
~~~~~~~~~~~~~~~~~~~~~~


<pre>
Let D be the number of dimes.

Then the number of pennies is 2D, according to the problem.

Hence, the number of nickels is (27 - D - 2D) = 37-3D  (the remaining coins).



Now write the total money equations, in cents

    5*(37-3D) + 10*D + 2D = 155  cents.


    +-----------------------------------------------+
    |   At this point, the setup is just complete.  |
    +-----------------------------------------------+


Simplify this equation and find D

    185 - 15*D + 10*D + 2*D = 155

    -3*D = 155 - 185

    -3*D = -30

     D = {{{(-30)/(-3)}}} = 10.


<U>ANSWER</U>.  10 dimes, 20 pennies and 37-10-20 = 7 nickels.


<U>CHECK</U> for the total value  10*10 + 20*1 + 7*5 = 155 cents = $1.55.   ! correct !
</pre>

Solved using one equation in one unknown.