Coin Problems

Learn to turn coins into numbers and equations, then practice with fresh problems every time.

1. Coins are worth cents

The golden rule of coin problems: convert everything to cents first. Then value = (number of coins) × (value of one coin).

Notice the difference between how many coins (a count) and how much they’re worth (a value). Mixing these up is the #1 mistake.

Try it: click coins to drop them in the tray. Reach the target using as few coins as possible.

Total: 0¢Coins used: 0

Target:

2. Two kinds of coins, two equations

Problem: Maria has 12 coins, all nickels and dimes, worth 95¢. How many of each?

Step 1: Name the unknowns. Let d = number of dimes. Let n = number of nickels.

Step 2: Count equation. n + d = 12, so n = 12 − d.

Step 3: Value equation (in cents). 5n + 10d = 95.

Step 4: Substitute. 5(12 − d) + 10d = 95 → 60 − 5d + 10d = 95 → 5d = 35 → d = 7.

Step 5: Finish and check. n = 12 − 7 = 5. Check: 5(5) + 10(7) = 25 + 70 = 95¢ ✓ and 5 + 7 = 12 coins ✓.

Guess-and-check view. Slide the number of dimes and watch the total value change. Which value hits 95¢?

Dimes	Nickels	Dime value	Nickel value	Total

3. How many ways to make change?

Here the question changes: not “how many of each?” but “how many different combinations add up to the amount?” Pick the allowed coins and an amount.

Amount (¢):

Ways:

Strategy: go coin by coin. Fix how many quarters (0, 1, 2…), then see how the leftover can be made with dimes and nickels. Organized lists never miss a case.

4. Practice

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Quiz

Add players, pick who is playing, then take a 10-question quiz. Scores are saved in this browser only.

Difficulty Questions