2014 AMC 12B 第 1 题

Question

Leah 有

13

枚硬币，全部是一美分硬币和五美分硬币。如果她比现在多一枚五美分硬币，那么她的一美分硬币和五美分硬币数量就相同。Leah 的硬币一共值多少美分？

Leah has

13

coins, all of which are pennies and nickels. If she had one more nickel than she has now, then she would have the same number of pennies and nickels. In cents, how much are Leah’s coins worth?

33

35

37

39

41

答案：C

知识点：一次方程钱币

难度评级：920

小提示：

设

n

为五美分硬币的数量，则一美分硬币有

13-n

枚。

Let

n

be the number of nickels, so there are

13-n

pennies

大提示：

多一枚五美分硬币后有

n+1

枚，这应等于

13-n

枚一美分硬币。

Adding one nickel gives

n+1

nickels, which must equal the

13-n

pennies

解答：

设

n

为五美分硬币的数量，则 Leah 有

13-n

枚一美分硬币。多一枚五美分硬币后，她会有

n+1

枚五美分硬币，这等于一美分硬币的数量：

n+1 = 13-n\text{。}

解得

n=6

，所以她有

6

枚五美分硬币和

7

枚一美分硬币。

总价值为

6\cdot5 + 7 = 37

美分。

所以正确答案是 C。

Let

n

be the number of nickels, so Leah has

13-n

pennies. One more nickel would give her

n+1

nickels, and this equals the number of pennies:

n+1 = 13-n.

Solving gives

n=6,

so there are

6

nickels and

7

pennies.

The total value is

6\cdot5 + 7 = 37

cents.

Thus, the correct answer is C.

2014 AMC 12B 第 1 题

答案：C

难度评级：920

小提示：

大提示：

解答：

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