sat suite question viewer

Problem-Solving and Data Analysis / Percentages Difficulty: Hard

The positive number $a$ is $2,241 percent sign$ of the sum of the positive numbers $b$ and $c$ , and $b$ is $83 percent sign$ of $c$ . What percent of $b$ is $a$ ?

Back question 55 of 78 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78

Explanation

Choice D is correct. It’s given that $a$ is $2,241 percent sign$ of the sum of $b$ and $c$ . This can be represented by the equation $a = (\frac{2,241}{100}) (b + c)$ , or $a = 22.41 (b + c)$ . It’s also given that that $b$ is $83 percent sign$ of $c$ . This can be represented by the equation $b = (\frac{83}{100}) c$ , or $b equals 0.83 c$ . Dividing both sides of this equation by $0.83$ yields $\frac{b}{0.83} = c$ . Substituting $StartFraction b Over 0.83 EndFraction$ for $c$ in the equation $a = 22.41 (b + c)$ yields $a = 22.41 (b + \frac{b}{0.83})$ , or $a = 22.41 (\frac{1.83 b}{0.83})$ , which is equivalent to $a = \frac{41.0103 b}{0.83}$ , or $a equals 49.41 b$ . This equation is equivalent to $a = (\frac{4,941}{100}) b$ ; therefore, $a$ is $4,941 percent sign$ of $b$ .

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

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

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