A box contains 54 coins, which are either 20-cent coins or 50-cent coins. If the total value is $20.70, find the number of 20-cent coins.

Correct answer: 21. With x 20-cent coins and 54 − x 50-cent coins: 0.20x + 0.50(54 − x) = 20.70, so x = 21. Check: 21 × 0.20 + 33 × 0.50 = 20.70.

Background: Problems with two unknown quantities need two equations: one for the count (x + y = 54) and one for the total value (0.20x + 0.50y = 20.70).

• 17: 17 does not satisfy the value equation.
• 19: 19 does not satisfy the value equation.
• 25: 25 does not satisfy the value equation.

Did you know? You can always check an answer by substituting it back: 21 × 0.20 + 33 × 0.50 = 20.70.

Memory trick: One equation for count, one for value.