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Problem-Solving and Data Analysis / Percentages Difficulty: Hard

The number $w$ is $110 percent sign$ greater than the number $z$ . The number $z$ is $55 percent sign$ less than $50$ . What is the value of $w$ ?

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Explanation

The correct answer is $47.25$ . It’s given that the number $w$ is $110 percent sign$ greater than the number $z$ . It follows that $w = (1 + \frac{110}{100}) z$ , or $w equals 2.1 z$ . It’s also given that the number $z$ is $55 percent sign$ less than $50$ . It follows that $z = (1 - \frac{55}{100}) (50)$ , or $z equals 0.45 left parenthesis 50 right parenthesis$ , which yields $z equals 22.5$ . Substituting $22.5$ for $z$ in the equation $w equals 2.1 z$ yields $w equals 2.1 left parenthesis 22.5 right parenthesis$ , which is equivalent to $w equals 47.25$ . Therefore, the value of $w$ is $47.25$ . Note that 47.25 and 189/4 are examples of ways to enter a correct answer.