   SEARCH HOME Math Central Quandaries & Queries  Question from a student: Please help me me find the answer to the following question. Thank you: Sally empties his jar of coins. It contains $3.75 in nickels, dimes, and quarters. The number of dimes is twice the number of nickels and the number of quarters is three less than the number of nickels. Determine how many nickels, dimes, and quarters were in the in the jar. Hi there. This is a question with three unknown amounts and three relationships between them. First you need to come up with the three equations. Let's say N = the number of nickels, D is dimes and Q is quarters. Then we know the total amount is$3.75, so

3.75 = 0.05N + 0.10D + 0.25Q. That's equation one.

Also, the number of dimes is twice the number of nickels, so

D = 2N. That's equation two.

Also, the number of quarters is three less than the number of nickels, so

Q = N - 3. And that's equation three.

Whenever you have three unknown amounts, you need three different equations if you want to be able to find the values of the unknowns. You have these.

You can easily substitute the values for D and Q (from the second and third equations) into the first equation:

3.75 = 0.05N + 0.10D + 0.25Q

becomes

3.75 = 0.05N + 0.10(2N) + 0.25(N-3).

Now you can just solve for N and use that to find D and Q.

Cheers,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.