The dimensions of a rectangle are $\sqrt{50 a^3 b^2}$ and $\sqrt{200 a^3}$. A student found the perimeter as follows: $\begin{aligned} 2 \sqrt{50 a^3 b^2}+2 \sqrt{200 a^3} & =2 \cdot 5 a b \sqrt{2 a}+2 \cdot 10 a \sqrt{2 a} \\ & =10 a b \sqrt{2 a}+20 a \sqrt{2 a} \\ & =30 a b \sqrt{2 a} \end{aligned}$ What is the student's error?
A. The student should not have multiplied each expression by two.
B. The student simplified $2 \sqrt{50 a^3 b^2}$ incorrectly.
C. The student simplified $2 \sqrt{200 a^3}$ incorrectly.
D. The student incorrectly simplified $10 a b \sqrt{2 a}+20 a \sqrt{2 a}$.
Answer (3)
Answer: 6 is the only multiple of three that would work. ;
You would multiply 12/2=6 6 ∗ 3 = 18 for 3 magazines
Ken can only buy magazines for $6 each, as it's the only multiple of $3 that fits into his total spending of $12 for two magazines.
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