Question

一个大披萨的 $\frac{1}{3}$ 加上 $3\frac{1}{2}$ 杯橙子片的重量，等于同一个大披萨的 $\frac{3}{4}$ 加上 $\frac{1}{2}$ 杯橙子片的重量。一杯橙子片重 $\frac{1}{4}$ 磅。一个大披萨重多少磅？

The weight of $\frac{1}{3}$ of a large pizza together with $3\frac{1}{2}$ cups of orange slices is the same as the weight of $\frac{3}{4}$ of a large pizza together with $\frac{1}{2}$ cup of orange slices. A cup of orange slices weighs $\frac{1}{4}$ of a pound. What is the weight, in pounds, of a large pizza?

$1\frac{4}{5}$

$2$

$2\frac{2}{5}$

$3$

$3\frac{3}{5}$

答案：A

知识点：一次方程分数

难度评级：1080

解答：

设披萨重量为 $p$ 。一杯橙子片重 $\frac14$ 磅，所以天平两边满足 $\frac13 p + \frac72 \cdot \frac14 = \frac34 p + \frac12 \cdot \frac14$ ，也就是 $\frac13 p + \frac78 = \frac34 p + \frac18$ 。整理披萨项得到 $\frac68 = \left(\frac34 - \frac13\right)p = \frac{5}{12}p$ 。因此 $p = \frac34 \cdot \frac{12}{5} = \frac95 = 1\frac45$ 。所以答案是 A。

Let $p$ be the pizza's weight. A cup of orange slices is $\frac14$ pound, so the two sides balance as $\frac13 p + \frac72 \cdot \frac14 = \frac34 p + \frac12 \cdot \frac14,$ that is $\frac13 p + \frac78 = \frac34 p + \frac18.$ Collect the pizza terms: $\frac68 = \left(\frac34 - \frac13\right)p = \frac{5}{12}p.$ So $p = \frac34 \cdot \frac{12}{5} = \frac95 = 1\frac45.$ Therefore, the answer is A.

2023 AMC 10A 第 2 题

答案：A

难度评级：1080

解答：

其他年份的第 2 题