i have 4.50 in change: 4more quarters than dimes, 3times as many nickels as dimes. how many coins of each type do i have?

Question

i have 4.50 in change: 4more quarters than dimes, 3times as many nickels as dimes. how many coins of each type do i have? 

Answer 1

Hi Lindsay--Ready?

 

First, you have a number of dimes we'll call d. Each one is worth 10 cents, so the value of your dimes will be 10d (for now...)

 

and although we could call your nickels n and your quarters q, we can also name them in terms of d. Like this:

 

each q = d + 4, and there are 25 cents per each of those, so that's:

 

25(d + 4), or 25d + 100

 

and each n = 3 x d, and there are 5 cents per each of these, so that's:

 

5(3d), or 15d.

 

Now, you add up all those d's: 10d + 25d + 15d, PLUS the 100, and it all adds up to 450 cents. Like this:

 

10d + 25d + 15d + 100 = 450. Then combine terms like this:

 

50d + 100 = 450, so 50d = 350.

 

Divide the 50 out of both sides, and you get d = 7.

 

Therefore, there are 7 dimes, 11 quarters, and 21 nickels.

 

If we did this right, all those coins will add up to 450 cents. (They do :-)  )

 

Hope this is helpful!

 

Matt