# At a Glance - Coin Problems

There are some problems where we need to be careful to differentiate between the *number* of something we have and the *value* of something. If someone asks how much change you've got on you and you say 75, does that mean you have 75 cents or 75 coins? If it's the latter, you could have $75 if they're all silver dollars. Either way, you should probably tell your friend you only have 75 cents, so he doesn't take advantage of you.

### Sample Problem

Lois has two more nickels than she has quarters. She has one dollar in all. How many nickels does she have?

First of all, here's what we know:

(amount of money Lois has) = (amount of money Lois has in nickels) + (amount of money Lois has in quarters)

We also know that:

(amount of money Lois has in quarters) = 0.25(number of quarters Lois has) = 0.25*q*

...where *q* is the number of quarters Lois has. Where did we find that number, you ask? A quarter is worth 25 cents, you see. Ask a silly question, get a silly answer.

Since Lois has two more nickels than she has quarters, we can also write:

(amount of money Lois has in nickels) = 0.05(*q* + 2)

Lois has one dollar total. Putting all our information together, we can rewrite our first equation:

1 = 0.05(*q* + 2) + 0.25*q*

Solving for *q*, we find *q* = 3. Since "she has three quarters'' doesn't answer the question "how many nickels does Lois have?'' we need to do one more step: Lois has two more nickels than quarters, so she has 3 + 2 = 5 nickels. See how it helps to take one last look at what the problem's asking you to find? Phew. We almost had a national crisis on our hands.