AMC8 2011

AMC8 2011 · Q3

AMC8 2011 · Q3. It mainly tests Basic counting (rules of product/sum), Area & perimeter.

Extend the square pattern of 8 black and 17 white square tiles by attaching a border of black tiles around the square. What is the ratio of black tiles to white tiles in the extended pattern?

将由 8 个黑色和 17 个白色方形瓷砖组成的正方形图案扩展，在正方形周围附加一层黑色瓷砖边框。扩展图案中黑色瓷砖与白色瓷砖的比率为多少？

(A) 8 : 17 8 : 17

(B) 25 : 49 25 : 49

(D) 32 : 17 32 : 17

(E) 36 : 17 36 : 17

Answer

Correct choice: (D)

正确答案：（D）

Solution

One way of approaching this is drawing the next circle of boxes around the current square. We can now count the number of black and white tiles; 32 black tiles and 17 white tiles. This means the answer is $\boxed{\textbf{(D) }32:17}$.

一种方法是在当前正方形周围画出下一层方框。现在可以数出黑色和白色瓷砖的数量；32 个黑色瓷砖和 17 个白色瓷砖。因此答案是 $\boxed{\textbf{(D) }32:17}$。

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