AlgebraMediumCoins from a count and a value
Algebra practice question
A purse holds 30 coins, all nickels (5 cents) and dimes (10 cents), with a total value of $2.20. How many of the coins are dimes?
Answer: 14
Let d be dimes and n nickels: n + d = 30 and 5n + 10d = 220. Substitute n = 30 − d: 150 − 5d + 10d = 220, so 5d = 70 and d = 14. Check: 16 nickels (80¢) + 14 dimes ($1.40) = $2.20.
Common wrong answers
- If you answered 16
- 16 is the number of NICKELS.
- If you answered 22
- 22 is 220/10, as if every coin were a dime — but then there would be only 22 coins.
- If you answered 44
- 44 is 220/5, as if every coin were a nickel.
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