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

Question

coin word problem. collected $30.25 in one day. two times as many dimes as nickles, how many OF EACH?

Answer 1

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.