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An orginization collected $30.25, there are two times as many dimes as nickles, how many are there of each?

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1 Answer

Hi Ashley,
 
To solve this question, we first come up with a formula representing the dollar amount given n nickels and d dimes. Nickels are worth $0.05 each, and dimes $0.10 each. No suprise here. So, the total dollar amount D, given n nickels and d dimes, can be expressed as:
 
D=0.05n + 0.10d
 
We have that the orginization collected $30.25 in one day, so
 
30.25 = 0.05n + 0.10d
 
Also, we know that there are twice as many dimes as nickels, so
 
d = 2n
 
Now, if we substitute our expression for d into our total dollar amount equation, we have
 
30.25 = 0.05n + 0.10d
 
          = 0.05n + 0.10(2n)
 
          = 0.05n + 0.20n
 
          = 0.25n
 
Solving for n, we find that
 
n = 30.25/.25
 
   = 121
 
There are twice as many dimes as nickels, so
 
d = 2n
 
   = 2(121)
 
   = 242
 
So, there are 121 nickels and 242 dimes. This is easily checked, as 242 dimes makes $24.20, and 121 nickels makes $6.05, and that $24.20 + $6.05 = $30.25.