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Problem-Solving and Data Analysis Difficulty: Hard

The number $a$ is $70 percent sign$ less than the positive number $b$ . The number $c$ is $80 percent sign$ greater than $a$ . The number $c$ is how many times $b$ ?

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Explanation

The correct answer is $.54$ . It's given that the number $a$ is $70 percent sign$ less than the positive number $b$ . Therefore, $a = (1 - \frac{70}{100}) b$ , which is equivalent to $a = (1 - 0.70) b$ , or $a equals 0.30 b$ . It's also given that the number $c$ is $80 percent sign$ greater than $a$ . Therefore, $c = (1 + \frac{80}{100}) a$ , which is equivalent to $c = (1 + 0.80) a$ , or $c equals 1.80 a$ . Since $a equals 0.30 b$ , substituting $0.30 b$ for $a$ in the equation $c equals 1.80 a$ yields $c equals 1.80 left parenthesis 0.30 b right parenthesis$ , or $c equals 0.54 b$ . Thus, $c$ is $0.54$ times $b$ . Note that .54 and 27/50 are examples of ways to enter a correct answer.