AMC10 2023 A

AMC10 2023 A · Q2

AMC10 2023 A · Q2. It mainly tests Systems of equations, Fractions.

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?

一大块披萨的 $\frac{1}{3}$ 加上 $3 \frac{1}{2}$ 杯橙子片的分量，与一大块披萨的 $\frac{3}{4}$ 加上 $\frac{1}{2}$ 杯橙子片的分量相同。一杯橙子片重 $\frac{1}{4}$ 磅。大披萨的重量是多少磅？

(A) 1\frac{4}{5} 1\frac{4}{5}

(B) 2 2

(D) 3 3

(E) 3\frac{3}{5} 3\frac{3}{5}

Answer

Correct choice: (A)

正确答案：（A）

Solution

Use a system of equations. Let $x$ be the weight of a pizza and $y$ be the weight of a cup of orange slices. We have \[\frac{1}{3}x+\frac{7}{2}y=\frac{3}{4}x+\frac{1}{2}y.\] Rearranging, we get \begin{align*} \frac{5}{12}x&=3y, \\ x&=\frac{36}{5}y. \end{align*} Plugging in $\frac{1}{4}$ pounds for $y$ by the given gives $\frac{9}{5}=\boxed{\textbf{(A) }1\frac{4}{5}}.$

使用方程组。让 $x$ 表示披萨的重量，$y$ 表示一杯橙子片的重量。我们有 \[\frac{1}{3}x+\frac{7}{2}y=\frac{3}{4}x+\frac{1}{2}y.\] 整理得 \begin{align*} \frac{5}{12}x&=3y, \\ x&=\frac{36}{5}y. \end{align*} 代入已知 $y=\frac{1}{4}$ 磅，得 $\frac{9}{5}=\boxed{\textbf{(A) }1\frac{4}{5}}.$

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