SOLUTION: Eddie spills his cash register drawer on the floor and has to sweep up the coins. He has 680 coins, which are a mixture of pennies, nickels, dimes, and quarters. There are 10 times

Question 345372: Eddie spills his cash register drawer on the floor and has to sweep up the coins. He has 680 coins, which are a mixture of pennies, nickels, dimes, and quarters. There are 10 times as many pennies as dimes, and half as many quarters as dimes. If he has $25.00, how many dimes are there?
Answer by Edwin McCravy(20077) (Show Source): You can put this solution on YOUR website!
Eddie spills his cash register drawer on the floor and has to sweep up the coins. He has 680 coins, which are a mixture of pennies, nickels, dimes, and quarters. There are 10 times as many pennies as dimes, and half as many quarters as dimes. If he has $25.00, how many dimes are there?

>>...He has 680 coins, which are a mixture of pennies, nickels, dimes,
and quarters...<<

>>...There are 10 times as many pennies as dimes,...<<

>>...half as many quarters as dimes...<<

>>...he has $25.00...<<




   

Substitute 10D for P, and  for Q in the first 
equation:






Clear of fractions by multiplying through by 2





Divide through by 5



-----

Substitute 10D for P, and  for Q in the fourth
equation:






Clear of fractions by multiplying through by 2





Now we have this system of two equations in 2 unknowns:



Solve that and get 36 dimes and 266 nickels.

So the answer is 36 for the number of dimes.

However in order to check the problem, we need to find 

the number of pennies and quarters.













360 pennies, 266 nickels, 36 dimes, 18 quarters

Checking:

>>...He has 680 coins,...<<


Checking: 360+266+36+18 = 680

That checks.

>>...There are 10 times as many pennies as dimes,...<<


Checking 360 is 10 times 36

That checks.

>>...half as many quarters as dimes...<<


Checking: 18 is half of 36.

That checks

>>...he has $25.00...<<


360 pennies = 360($.10) = $ 3.60
266 nickels = 266($.05) = $13.30
36 dimes = 36($.10)     = $ 3.60 
18 quarters = 18($.25)  = $ 4.50
--------------------------------
                  Total = $25.00

That checks.

Answer: 36 dimes.

Edwin

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