AMC8 2000

AMC8 2000 · Q20

AMC8 2000 · Q20. It mainly tests Money / coins, Casework.

You have nine coins: a collection of pennies, nickels, dimes, and quarters having a total value of $1.02$, with at least one coin of each type. How many dimes must you have?

你有九枚硬币：便士、镍币、角币和25分币，总价值1.02美元，且至少有一种每种类型。必须有多少个角币？

(A) 1 1

(B) 2 2

(D) 4 4

(E) 5 5

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): Since the total value is \$1.02, you must have either 2 or 7 pennies. It is impossible to have 7 pennies, since the two remaining coins cannot have a value of 95 cents. With 2 pennies the remaining 7 coins have a value of \$1.00. Either 2 or 3 of these must be quarters. If you have 2 quarters, the other 5 coins would be dimes, and you would have no nickels. The only possible solution is 3 quarters, 1 dime, 3 nickels and 2 pennies.

答案（A）：由于总价值为 \$1.02，你必须有 2 枚或 7 枚便士。拥有 7 枚便士是不可能的，因为剩下的两枚硬币不可能组成 95 美分。若有 2 枚便士，则其余 7 枚硬币的总值为 \$1.00。在这 7 枚中，必须有 2 枚或 3 枚是 25 美分硬币（quarter）。如果有 2 枚 quarter，那么另外 5 枚硬币就会都是 10 美分硬币（dime），从而不会有 5 美分硬币（nickel）。唯一可能的解是：3 枚 quarter、1 枚 dime、3 枚 nickel 和 2 枚 penny。

Topics