Question 1119320
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A boy has 180 coins altogether. There are nickels dimes and quarters. Number of dimes is half the number of nickels and quarters. 
Value of coins is 16 {{{highlight(dollars)}}}. How many of each kind of coin does he have
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Let x be the number of dimes.

Then the number of nickels and dimes (altogether) is 2x, according to the condition.


The total number of coins is 180 = x + 2x = 3x,  which implies that the number of dimes is  x = {{{180/3}}} = 60.


Thus you conclude that total number of nickels and quarters is 180 - 60 = 120, and their value is  16-60*0.1 = 10 dollars.


Now, let Q be the unknown number of quarters.

Then the number of nickels is (120-Q), and the value equation for nickels and quarters is


    5*(120-Q) + 25Q = 1000    (cents,  or $10).


Simplify and solve for Q:

    600 - 5Q + 25Q = 1000,

    20Q = 1000 - 600 = 400  ====>  Q = {{{400/20}}} = 20.


<U>Answer</U>.  20 quarters, (120-20) = 100 nickels and 60 dimes.
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Solved.