If Donald has 3 times as many nickels as dimes and they have a combined value of 200 cents, how many of each coin does he have?

Question

If Donald has 3 times as many nickels as dimes and they have a combined value of 200 cents, how many of each coin does he have?

Answer 1

let the number of dimes be x

 

therefore the number of nickels would be 3x

 

summing their value 10x + 5*3x = 200

 

therefore 25x = 200

 

therefore x = 200/25 = 8

 

there are 8 dimes and 24 nickles

 

checking; 8*10 + 24*5 = 80 + 120 = 200 (proven)

Answer 2

Let's say Donald has x nickels and y dimes.

Since nickel is 5 cents, he would have 5x cents in nickels.

Similarly, since dime is 10 cents, he would have 10y cents in dimes.

Total: 5x+10y = 200

 

Since you have two variables, you need two equations to solve this. You know that "Donald has 3 times as many nickels as dimes."

We can write it as 3y = x.

 

Therefore, in the first equation we can substitute 3y instead of x:

5(3y)+10y = 200.

 

Now you can solve for y, and then x!

 

Answer 3

Hi Kelsy,

 

Pick two variables to represent the number of nickels and dimes Donald has:

 

     n = number of nickels

     d = number of dimes

 

The total value of all of Donald's coins is 200 cents. The value (in cents) of n nickels is just 5 times n, and the value (in cents) of d dimes is just 10 times d:

 

     200 = 5n + 10d

 

But Donald has three times as many nickels as he has dimes:

 

     n = 3d

 

So if you plug in 3d for n in the total value equation above:

 

     200 = 5(3d) + 10d

 

You can solve for d. Once you've got that, you can plug d back into either equation to solve for n.

 

Hope this helps!  :)