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Problem-Solving and Data Analysis / Percentages Difficulty: Hard

The number $a$ is $60 percent sign$ greater than the positive number $b$ . The number $c$ is $45 percent sign$ less than $a$ . The number $c$ is how many times $b$ ?

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Explanation

The correct answer is $.88$ . It’s given that the number $a$ is $60 percent sign$ greater than the positive number $b$ . Therefore, $a = (1 + \frac{60}{100}) b$ , which is equivalent to $a = (1 + 0.60) b$ , or $a equals 1.60 b$ . It’s also given that the number $c$ is $45 percent sign$ less than $a$ . Therefore, $c = (1 - \frac{45}{100}) a$ , which is equivalent to $c = (1 - 0.45) a$ , or $c equals 0.55 a$ . Since $a equals 1.60 b$ , substituting $1.60 b$ for $a$ in the equation $c equals 0.55 a$ yields $c equals 0.55 left parenthesis 1.60 b right parenthesis$ , or $c equals 0.88 b$ . Thus, the number $c$ is $0.88$ times the number $b$ . Note that .88 and 22/25 are examples of ways to enter a correct answer.