AMC8 2022

AMC8 2022 · Q11

AMC8 2022 · Q11. It mainly tests Linear equations, Arithmetic misc.

Henry the donkey has a very long piece of pasta. He takes a number of bites of pasta, each time eating $3$ inches of pasta from the middle of one piece. In the end, he has $10$ pieces of pasta whose total length is $17$ inches. How long, in inches, was the piece of pasta he started with?

亨利驴有一根很长的意大利面。他咬了好几口，每次从一根面的中间吃掉3英寸。在最后，他有10根意大利面，总长度是17英寸。他开始的那根意大利面有多长（英寸）？

(A) 34 34

(B) 38 38

(D) 44 44

(E) 47 47

Answer

Correct choice: (D)

正确答案：（D）

Solution

Let's say that the first strand of pasta he had is x. The first time he takes a bite of this strand will make it 2 pieces. This is x - 3. The second time he takes the bites of EACH strand will become (x - 3) * 3(2). The 2 is for the two bites he took, 1 for each strand. This equation is showing that for every bite that he is taking, he is taking off 3 inches. This is being showed in the 3(2). He took 2 bites, each taking off 3 inches. Now, the problem is stating that their are 10 pieces of pasta and the TOTAL length is 17 inches. We have to plug in the total number of bites to the equation (x - 3) * 3( ). To find this out, we can see that for the number of strands there are, he took 1 less bite than that number. For example, if there are 2 pieces, he took 1 bite to get those. Since there are 10 pieces, he took 9 bites. The equation then becomes, (x - 3) * 3(9) = 17. To solve this, x = 44. Therefore, the answer is $\boxed{\textbf{(D) } 44}$.

假设他开始的第一根意大利面的长度是$x$。第一次咬这根面会把它分成2根，总长度为$x-3$。第二次他咬每一根面，会把每根变成2根，每次咬掉3英寸。注意到，每咬一口，面条件数增加1。最终有10根，所以咬了9口。每咬一口吃掉3英寸，总共吃掉$9\times3=27$英寸。最终总长度17英寸，所以原长度$x=17+27=44$。因此答案是\boxed{\textbf{(D) } 44}。

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