SOLUTION: A collection of nickels, dimes, and quarters consist of 95 coins with a total of $ 10.75 . If there are 2 times as many dimes as quarters, find the number of each type

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Question 1119944: A collection of nickels, dimes, and quarters consist of
95
coins with a total of
$
10.75
. If there are
2
times as many dimes as quarters, find the number of each type of coins.
There are
nickels,
dimes and
quarters.
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
It is typical one-unknown problem.


Let x be the number of quarters.


Then the number of dimes is 2x, according to the condition.


Then the number of nickels must be (95-(x+2x)) = (95-3x).


The money equation is


   5*(95-3x) + 10*(2x) + 25*x = 1075 cents.


Simplify and solve for x:


    5*95 - 15x + 20x + 25x = 1075

    30x = 1075 - 5*95 

    30x = 600  ====>  x = 600%2F30 = 20.


Answer.  20 quarters,  2*20 = 40 dimes and  (95 - 20 - 40) = 35 nickels.

Solved.