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Problem-Solving and Data Analysis / Percentages Difficulty: Hard

A scientist studying the life cycle of dragonflies counted the number of dragonflies in a certain habitat each day for $46$ days. On February $15$ , there were $99$ dragonflies in the habitat. The percent increase in the number of dragonflies in the habitat from January $1$ to February $15$ was $12.50 percent sign$ . How many dragonflies were in the habitat on January $1$ ?

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Explanation

Choice A is correct. It’s given that a scientist studying the life cycle of dragonflies counted the number of dragonflies in a certain habitat each day for $46$ days. It’s also given that on February $15$ , there were $99$ dragonflies in the habitat and that the percent increase in the number of dragonflies in the habitat from January $1$ to February $15$ was $12.50 percent sign$ . This can be represented by the equation
$99 = (1 + \frac{12.50}{100}) x$ , where $x$ represents the number of dragonflies in the habitat on January $1$ . This equation can be rewritten as $99 equals 1.125 x$ . Dividing both sides of this equation by $1.125$ yields $88 equals x$ . Therefore, there were $88$ dragonflies in the habitat on January $1$ .

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.