If Kyle has 4 times as many nickels as dimes and they have a combined value of 120 cents, how many of each coin does he have?

Question

If Kyle has 4 times as many nickels as dimes and they have a combined value of 120 cents, how many of each coin does he have?

Answer 1

Hi Rashad.

 

The problem states that Kyle has 4 times as many nickels as dimes.  So for each dime, Kyle has 4 nickels.

 

1 DIme ==> 4 Nickels    or   10 + 20 = 30 cents

2 Dimes ==>  8 Nickels  or  20 + 40 = 60 cents

3 Dimes ==>  12 Nickels  or  30 + 60 = 90 cents

4 Dimes ==>  16 Nickels or 40 + 80 = 120 cents

 

And we have found our solution:  We need 4 dimes and 16 nickels.

 

Algebraically, notice from the list above that The number of nickels is always 4 * the number of dimes.  So if we use D for dimes and N for nickels we have 4*D=N

 

So the money associated with nickels and dimes would be

 

5*Nickels + 10*Dimes = total amount of money

 

5N + 10D=120

 

Using N=4D;

 

5(4D) + 10D = 120

 

20D + 10D = 120

 

30D = 120

 

D=4

 

So we need 4 dimes and 4 times that many nickels, of 16 nickels, just like we found when we made the list above.