SOLUTION: Peter collected 105 coins. All the coins are nickels,dimes or quarters. Three times the number of nickels is the same as twice the number of dimes. The value of the coins is $22.

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Question 56180: Peter collected 105 coins. All the coins are nickels,dimes or quarters. Three times the number of nickels is the same as twice the number of dimes. The value of the coins is $22.00. Find the number of nickels, dimes and quarters that Peter has.

Could you please tell me the formulas to solve this, I can solve the other problems I have to complete that are similar.I've tried for a couple of hours, can't seem to understand the logic. Thanks for your help.

I do not have the testbook at home. My worksheet says Algebra II Systems of Linear Equations.

Answer by stanbon(57282) (Show Source):
You can put this solution on YOUR website!
Peter collected 105 coins. All the coins are nickels,dimes or quarters. Three times the number of nickels is the same as twice the number of dimes. The value of the coins is $22.00. Find the number of nickels, dimes and quarters that Peter has.
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Let "x" be the number of dimes; Value of those is 10x cents.
Since 3(Number of nickels) is 2x,
Number of nickels =(2/3)x ; Value is 5(2/3x)=(10/3)x cents
Number of quarters is 105-x-(2/3)x=105-(5/3)x;
Value is 25(105-(5/3)x=2625-(125/3)x cents
EQUATION:
value + value + value = 2200 cents
10x+(10/3)x+ 2625-(125/3)x = 2200
(-85/3)x=-425
x=15 (number of dimes)
(2/3)x=10 (number of nickels)
105-(5/3)x=80 (number of quarters)
Cheers,
Stan H>