2021 AMC 10A Spring Problem 2

Attempt Problem 2 of the 2021 AMC 10A Spring below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2021 AMC 10A Spring solutions, or check the answer key.

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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?

$600$

$650$

$1950$

$2000$

$2050$

Answer: C

Concepts:ratio and proportion linear equation

Difficulty rating: 560

Solution:

Let $x$ be the number of students in Lara's high school. Then Portia's high school has $3x$ students.

Therefore, $\begin{aligned} 3x + x &= 2600 \\ x &= 650. \end{aligned}$ Then $3x = 1950.$

Thus, C is the correct answer.

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