Question 1179758
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there were 24 nickles, dimes, and quarters whose total value equaled $4.25. 
how many coins of each kind were there if the number of nickels equaled the number of dimes?
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        Here is very simple way to solve this problem for 3 unknowns using only one equation.



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Let x be the number of nickels.

Then the number of dimes also is x, according to the problem.


Then the number of quarters is  24-x-x = 24-2x.


Now write the total money equation

    5x + 10x + 25*(24-2x) = 425  cents.


Simplify and find x

    15x + 600 - 50x = 425

    600 - 425 = 50x - 15x

       175    =    35x

         x    =     175/35 = 5.


<U>ANSWER</U>.  5 nickels, 5 dimes and 24-5-5 = 14 quarters.


<U>CHECK</U>  for the total money  5*5 + 5*10 + 14*25 = 425 cents.   ! correct !
</pre>

Solved completely, using only one equation.