Question

Maddy 和 Lara 看到黑板上写着一列数。Maddy 给列表中的每个数加上 $3$ ，发现新数之和为 $45$ 。Lara 把列表中的每个数乘以 $3$ ，发现新数之和也为 $45$ 。黑板上写了多少个数？

Maddy and Lara see a list of numbers written on a blackboard. Maddy adds $3$ to each number in the list and finds that the sum of her new numbers is $45.$ Lara multiplies each number in the list by $3$ and finds that the sum of her new numbers is also $45.$ How many numbers are written on the blackboard?

$10$

$5$

$6$

$8$

$9$

答案：A

知识点：方程组求和

难度评级：1130

解答：

设原数之和为 $S$ ，数的个数为 $n$ 。Maddy 每个数加 $3$ ，总和为 $S + 3n = 45$ 。Lara 把每个数变为原来的三倍，所以 $3S = 45$ ，得 $S = 15$ 。因此 $15 + 3n = 45$ ，所以 $n = 10$ 。所以正确答案是 A。

Let $S$ be the original sum and $n$ the number of entries. Maddy adds $3$ to each, so her total is $S + 3n = 45.$ Lara triples each, so hers is $3S = 45,$ giving $S = 15.$ Then $15 + 3n = 45,$ so $n = 10.$ Thus, A is the correct answer.

2023 AMC 10B 第 5 题

答案：A

难度评级：1130

解答：

其他年份的第 5 题