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Problem-Solving and Data Analysis / Percentages Difficulty: Hard

The number $a$ is $110 percent sign$ greater than the number $b$ . The number $b$ is $90 percent sign$ less than $47$ . What is the value of $a$ ?

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Explanation

The correct answer is $9.87$ . It’s given that the number $a$ is $110 percent sign$ greater than the number $b$ . It follows that $a = (1 + \frac{110}{100}) b$ , or $a equals 2.1 b$ . It’s also given that the number $b$ is $90 percent sign$ less than $47$ . It follows that $b = (1 - \frac{90}{100}) (47)$ , or $b equals 0.1 left parenthesis 47 right parenthesis$ , which yields $b equals 4.7$ . Substituting $4.7$ for $b$ in the equation $a equals 2.1 b$ yields $a equals 2.1 left parenthesis 4.7 right parenthesis$ , which is equivalent to $a equals 9.87$ . Therefore, the value of $a$ is $9.87$ .