Question

Patty 有 $20$ 枚硬币，由五分硬币和十分硬币组成。如果她的五分硬币都变成十分硬币，而十分硬币都变成五分硬币，她会多 $70$ 美分。她现在的硬币总值是多少？

Patty has $20$ coins consisting of nickels and dimes. If her nickels were dimes and her dimes were nickels, she would have $70$ cents more. How much are her coins worth?

$\$1.15$

$\$1.20$

$\$1.25$

$\$1.30$

$\$1.35$

答案：A

知识点：方程组钱币

难度评级：1240

解答：

交换后价值增加，所以 Patty 的五分硬币比十分硬币多。每枚硬币交换后价值变化 $5$ 美分，所以五分硬币比十分硬币多 $70 / 5 = 14$ 枚。

两种硬币的数量满足 $n + d = 20$ 和 $n - d = 14$ ，解得她有 $17$ 枚五分硬币和 $3$ 枚十分硬币。

她的硬币总值为 $17 \cdot 5 + 3 \cdot 10 = 115$ 美分，即 $\$1.15$ 。

所以正确答案是 A。

Swapping increases the value, so Patty has more nickels than dimes. Each swapped coin changes the total by $5$ cents, so she has $70 / 5 = 14$ more nickels than dimes.

With $n + d = 20$ and $n - d = 14,$ she has $17$ nickels and $3$ dimes.

Her coins are worth $17 \cdot 5 + 3 \cdot 10 = 115$ cents, or $\$1.15.$

Thus, the correct answer is A.

2004 AMC 10B 第 15 题

答案：A

难度评级：1240

解答：

其他年份的第 15 题