# 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 have on them 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, we know that

(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, receive a silly answer.

Since Lois has two more nickels than she has quarters,

(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 as

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

Solving, 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 5 nickels. See how it helps to take one last look at what the problem is asking you to find? Phew. We almost had a national crisis on our hands.