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Algebra Difficulty: Easy

In $2010$ , a swim club had a total of $35$ swimmers, each classified as either advanced or intermediate. From $2010$ to $2020$ , the number of advanced swimmers in the club increased by approximately $53 percent sign$ , and the number of intermediate swimmers in the club increased by approximately $44 percent sign$ . The total number of swimmers in the club increased by approximately $49 percent sign$ . Which equation best represents this situation, where $a$ represents the number of advanced swimmers in the club in $2010$ and $b$ represents the number of intermediate swimmers in the club in $2010$ ?

$1.53 a + 1.49 b = 35 (1.44)$

$1.49 a + 0.53 b = 35 (1.44)$

$1.53 a + 1.44 b = 35 (1.49)$

$1.44 a + 1.53 b = 35 (1.49)$

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Explanation

Choice C is correct. It’s given that in $2010$ , a swim club had a total of $35$ swimmers, each classified as either advanced or intermediate, and that $a$ represents the number of advanced swimmers in $2010$ and $b$ represents the number of intermediate swimmers in $2010$ . It's also given that from $2010$ to $2020$ , the number of advanced swimmers in the club increased by approximately $53 percent sign$ and the number of intermediate swimmers in the club increased by approximately $44 percent sign$ . Thus, in $2020$ , the approximate number of advanced swimmers in the club can be represented as $1.53 a$ and the approximate number of intermediate swimmers in the club can be represented as $1.44 b$ . It's given that the total number of swimmers in the club increased by approximately $49 percent sign$ from $2010$ to $2020$ . Since the club had $35$ swimmers in $2010$ , it follows that the total number of swimmers in $2020$ can be represented as $35 left parenthesis 1.49 right parenthesis$ . Since the sum of the number of advanced swimmers in $2020$ and the number of intermediate swimmers in $2020$ equals the total number of swimmers in $2020$ , the equation $1.53 a + 1.44 b = 35 (1.49)$ best represents this situation.

Choice A is incorrect. This equation represents a situation where the number of intermediate swimmers in the club in $2020$ increased by approximately $49 percent sign$ , not $44 percent sign$ , and the total number of swimmers in the club in $2020$ increased by approximately $44 percent sign$ , not $49 percent sign$ .

Choice B is incorrect and may result from conceptual errors.

Choice D is incorrect. This equation represents a situation where the number of advanced swimmers in the club in $2020$ increased by approximately $44 percent sign$ , not $53 percent sign$ , and the number of intermediate swimmers in the club in $2020$ increased by approximately $53 percent sign$ , not $44 percent sign$ .