SOLUTION: A person has two times as many nickels as quarters. If the total face value of these coins is $3.50, how many of each type of coin does this person have?

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Question 530015: A person has two times as many nickels as quarters. If the total face value of these coins is $3.50, how many of each type of coin does this person have?
Found 2 solutions by Maths68, Edwin McCravy:
Answer by Maths68(1474)   (Show Source): You can put this solution on YOUR website!

Let
He has = x quarters
He has = 2x nickels

Total Amount = $3.50 or 3.50*100 = 350 cents

x*25+2x*5=350
25x+10x=350
35x=350
35x/35=350/35
x=10

He has = x = 10 quarters
He has = 2x = 2*10 = 20 nickels

Check
======
10*25 + 5*20 = 350
250+100=350
350=350
Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
The problem fails to state that the person has ONLY nickels and quarters.
As the problem is stated she could have some other coins as well.  For 
instance, she could have 7 dimes, 8 quarters and 16 nickels, and she would
still have $3.50 and twice as many nickels as quarters.  I just thought
I would point that out as it might be interesting if you mentioned it to
your teacher or classmates.  But I will assume that she has no other coins
but nickels and quarters. 

Assuming that she has ONLY nickels and quarters,

Let N = the number of quarters

Because of this statement:

>>...A person has two times as many nickels as quarters...<<

2N = the number of nickels.

To get our equation we use this principle:

  
    $.05 times  + $.25 times  = $3.50

                             .05(2N) + .25(N) = 3.50
                               5(2N) +  25(N) = 350
                                    10N + 25N = 350
                                          35N = 350 
                                            N = 10

So she has N = 10 quarters and 2N = 2(10) = 20 nickels.

Edwin
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