In a pile of coins, there are 15 more quarters than loonies. The total value of the coins is $21.25. How many quarters are there?

Question

Word problem using money. We can't seem to get the solution but know we need to include the value of the coins.  Please provide all steps to the correct answer please.

Answer 1

I think the wording is backwards. It should be "15 more loonies than quarters," and here's why:

 

first, know that a loony is a canadian dollar coin.

 

So the quarters can be 25q and the dollars can be 100d (let's work in cents for now).

 

And since each dollar is 4 quarters, 100d = 400q

 

So 425q = 2125 cents, which means q = 5.

 

5 quarters are worth 125 cents. 15 more than that = 20 loonies, which equals 2000 cents. Add 2000 + 125 and you get 2125 cents, or $21.25.

 

Hope this helps!

 

Matt in NY

Answer 2

What are loonies?

 

There's not enough information to solve this problem.

 

1) What is the money value for each loony

2) What is the total number of coins in the pile.

 

Let's just for fun set up a couple of equations.

 

L= the number of loonies

Q = L+15 = the number of quarters

 

Hence, L+Q=L+L+15=2L+15=total number of coins in the pile.

 

Let v=money value for each loony

 

Hence,

 

vL+0.25Q=vL+0.25(L+15)=vL+0.25L+3.75=(v+0.25)L+3.75=21.25

 

This implies L=(21.25-3.75)/(v+0.25)=17.5/(v+0.25)

 

Therefore the total number of quarters is:

 

Q = 17.5/(v+0.25) + 15 That is if you know what is v.

 

Moreover, it turns out you wouldn't necessarily need to know the total number of coins  given how many more quarters there are than loonies. It is good practice to set up the two equations.

 

For argument sake, lets assume the money value for loonies is v=0.

 

This implies the number of quarters is:

 

Q=17.5/(0+0.25)+15=70+15=85 Quarters LOL...