AMC10 2021 A

AMC10 2021 A · Q2

AMC10 2021 A · Q2. It mainly tests Systems of equations, Arithmetic misc.

Portia's high school has $3$ times as many students as Lara's high school. The two high schools have a total of $2600$ students. How many students does Portia's high school have?

Portia的高中有Lara高中的3倍学生。两所高中共有2600名学生。Portia的高中有多少学生？

(A) 600 600

(B) 650 650

(D) 2000 2000

(E) 2050 2050

Answer

Correct choice: (C)

正确答案：（C）

Solution

The following system of equations can be formed with $P$ representing the number of students in Portia's high school and $L$ representing the number of students in Lara's high school: \begin{align*} P&=3L, \\ P+L&=2600. \end{align*} Substituting $P=3L$ gives $4L=2600.$ Solving for $L$ gives $L=650.$ Since we need to find $P,$ we multiply $650$ by $3$ to get $P=\boxed{\textbf{(C)} ~1950}.$

可以用以下方程组表示，其中$P$表示Portia高中的学生数，$L$表示Lara高中的学生数： \begin{align*} P&=3L, \\ P+L&=2600. \end{align*} 代入$P=3L$得$4L=2600$。解得$L=650$。需要求$P$，所以$650\times3=\boxed{\textbf{(C)} ~1950}$。

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