Question

一个大披萨的 $\tfrac13$ 加上 $3\tfrac12$ 杯橙子片的重量，等于一个大披萨的 $\tfrac34$ 加上 $\tfrac12$ 杯橙子片的重量。一杯橙子片重 $\tfrac14$ 磅。一个大披萨重多少磅？

The weight of $\tfrac13$ of a large pizza together with $3\tfrac12$ cups of orange slices is the same as the weight of $\tfrac34$ of a large pizza together with $\tfrac12$ cup of orange slices. A cup of orange slices weighs $\tfrac14$ of a pound. What is the weight, in pounds, of a large pizza?

$1\tfrac45$

$2$

$2\tfrac25$

$3$

$3\tfrac35$

答案：A

知识点：一次方程分数

难度评级：1020

解答：

设披萨重 $P$ 磅。则 $3\tfrac12$ 杯重 $\tfrac72\cdot\tfrac14=\tfrac78$ 而 $\tfrac12$ 杯重 $\tfrac12\cdot\tfrac14=\tfrac18$ 。

方程为 $\tfrac13 P+\tfrac78=\tfrac34 P+\tfrac18.$

相减得 $\tfrac78-\tfrac18=\left(\tfrac34-\tfrac13\right)P$ ，所以 $\tfrac34=\tfrac{5}{12}P$ ，从而 $P=\dfrac{9}{5}=1\tfrac45$ 。

所以正确答案是 A。

Let the pizza weigh $P$ pounds. Then $3\tfrac12$ cups weigh $\tfrac72\cdot\tfrac14=\tfrac78$ and $\tfrac12$ cup weighs $\tfrac12\cdot\tfrac14=\tfrac18.$

The equation is $\tfrac13 P+\tfrac78=\tfrac34 P+\tfrac18.$

Subtracting gives $\tfrac78-\tfrac18=\left(\tfrac34-\tfrac13\right)P,$ so $\tfrac34=\tfrac{5}{12}P$ and $P=\dfrac{9}{5}=1\tfrac45.$

Thus, the correct answer is A.

2023 AMC 12A 第 2 题

答案：A

难度评级：1020

解答：

其他年份的第 2 题