2019 AMC amc8 真题 答案 详解

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中英双语真题

2019 AMC8
Problem 1
Ike and Mike go into a sandwich shop with a total of $30.00 to spend. Sandwiches cost $4.50 each and soft drinks cost $1.00 each. Ike and Mike plan to buy as many sandwiches as they can, and use any remaining money to buy soft drinks. Counting both sandwiches and soft drinks, how many items will they buy?
Ike 和 Mike 带着总共 30 美元去一家三明治商店，每块三明治价格 4.5 美元，每瓶软饮料价格 1 美元。Ike 和 Mike 打算尽可能多地买三明治，然后用剩下的钱去买软饮料，那么三明治和软饮料总个数加起来，他们将买多少件物品？
(A) 6 (B) 7 (C) 8 (D) 9 (E) 10

Problem 2
Three identical rectangles are put together to form rectangle ABCD, as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is 5 feet, what is the area in square feet of rectangle ABCD?
如图，把三个全等矩形拼在一起形成矩形 ABCD，已知每个小的矩形的短边为 5 英尺，求矩形 ABCD 的面积是多少平方英尺？
(A) 45 (B) 75 (C) 100 (D) 125 (E) 150

英文真题

Compiled on: January 1, 2021 AMC8 2019 Problems Page 10 of 109 Q1. Ike and Mike go into a sandwich shop with a total of $30.00 to spend. Sandwiches cost $4.50 each and soft drinks cost $1.00 each. Ike and Mike plan to buy as many sandwiches as they can and use the remaining money to buy soft drinks. Counting both soft drinks and sandwiches, how many items will they buy? A) 6 B) 5 C) 8 D) 9 E) 2 Q2. Three identical rectangles are put together to form rectangle ABCD, as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is 5 feet, what is the area in square feet of rectangle ABCD? A) 45 B) 75 C) 100 D) 125 E) 150 Q3. Which of the following is the correct order of the fractions (\frac{15}{11}, \frac{19}{15}), and (\frac{17}{13}), from least to greatest? A) (\frac{15}{11} < \frac{17}{13} < \frac{19}{15}) B) (\frac{15}{11} < \frac{19}{15} < \frac{17}{13}) C) (\frac{17}{13} < \frac{15}{11} < \frac{19}{15}) D) (\frac{19}{15} < \frac{17}{13} < \frac{15}{11}) E) (\frac{19}{15} < \frac{17}{13} < \frac{15}{11}) Q4. Quadrilateral ABCD is a rhombus with perimeter 52 meters. The length of diagonal AC is 24 meters. What is the area in square meters of rhombus ABCD? A) 60 B) 90 C) 105 D) 120 E) 144 Q5. A tortoise challenges a hare to a race. The hare eagerly agrees and quickly runs ahead, leaving the slow-moving tortoise behind. Confident that he will win, the hare stops to take a nap. Meanwhile, the tortoise walks at a slow steady pace for the entire race. The hare awakes and runs to the finish line, only to find the tortoise already there. Which of the following graphs matches the description of the race, showing the distance (d) traveled by the two animals over time (t) from start to finish?

真题文字详解(英文)

Problem 1

Ike and Mike go into a sandwich shop with a total of $30.00 to spend. Sandwiches cost $4.50 each and soft drinks cost $1.00 each. Ike and Mike plan to buy as many sandwiches as they can, and use any remaining money to buy soft drinks. Counting both sandwiches and soft drinks, how many items will they buy?

(A) 6 (B) 7 (C) 8 (D) 9 (E) 10

Solution 1

We know that the sandwiches cost $4.50 dollars. Guessing will bring us to multiplying $4.50 by 6, which gives us $27.00. Since they can spend $30.00 they have $3 left. Since soft drinks cost $1.00 dollar each, they can buy 3 soft drinks, which makes them spend $30.00. Since they bought 6 sandwiches and 3 soft drinks, they bought a total of 9 items. Therefore, the answer is (D) 9.

• SBose

Solution 2 (Using Algebra)

Let s be the number of sandwiches and d be the number of sodas. We have to satisfy the equation of:

$$4.50s + d = 30$$

In the question, it states that Ike and Mike buys as many sandwiches as possible. So we drop the number of sodas for a while. We have:

$$4.50s = 30$$ $$s = \frac{30}{4.5}$$ $$s = 6R3$$

We don't want a remainder so the maximum number of sandwiches is 6. The total money spent is $6 \cdot 4.50 = 27$. The number of dollar left to spent on sodas is $30 - 27 = 3$ dollars. 3 dollars can buy 3 sodas leading us to a total of $6 + 3 = 9$ items. Hence, the answer is (D) 9.

• by interactivemath

Problem 2

Three identical rectangles are put together to form rectangle ABCD, as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is 5 feet, what is the area in square feet of rectangle ABCD?

(A) 45 (B) 75 (C) 100 (D) 125 (E) 150

Solutions

Solution 1

We can see that there are 2 rectangles lying on top of the other and that is the same as the length of one rectangle. Now we know that the shorter side is 5, so the bigger side is 10, if we do $5 \cdot 2 = 10$. Now we get the sides of the big rectangle being 15 and 10, so the area is (E) 150.

~avamarora

Solution 2

Using the diagram we find that the larger side of the small rectangle is 2 times the length of the smaller side. Therefore, the longer side is $5 \cdot 2 = 10$. So the area of the identical rectangles is $5 \cdot 10 = 50$. We have 3 identical rectangles that form the large rectangle. Therefore the area of the large rectangle is $50 \cdot 3 = (E) 150.

~fath2012

Solution 3

真题文字详解(中英双语)

Problem 1

Ike and Mike go into a sandwich shop with a total of $30.00 to spend. Sandwiches cost $4.50 each and soft drinks cost $1.00 each. Ike and Mike plan to buy as many sandwiches as they can, and use any remaining money to buy soft drinks. Counting both sandwiches and soft drinks, how many items will they buy?

(A) 6 (B) 7 (C) 8 (D) 9 (E) 10

Solution 1

We know that the sandwiches cost $4.50 dollars. Guessing will bring us to multiplying 4.50 by 6, which gives us $27.00. Since they can spend $30.00 they have $3 left. Since soft drinks cost $1.00 each, they can buy 3 soft drinks, which makes them spend $30.00. Since they bought 6 sandwiches and 3 soft drinks, they bought a total of 9 items. Therefore, the answer is (D) 9.

• SBose

Solution 2 (Using Algebra)

解法 2（使用代数）

Let s be the number of sandwiches and d be the number of sodas. We have to satisfy the equation of

$$4.50s + d = 30$$

In the question, it states that Ike and Mike buys as many sandwiches as possible. So, we drop the number of sodas for a while. We have:

$$4.50s = 30$$

$$s = \frac{30}{4.5}$$

$$s = 6R3$$

We don't want a remainder so the maximum number of sandwiches is 6. The total money spent is $6 \cdot 4.50 = $27. The number of dollar left to spend on sodas is $30 - $27 = $3 dollars. $3 dollars can buy 3 sodas leading us to a total of $6 + 3 = 9$ items. Hence, the answer is (D) 9.

by interactivemath 由 interactivemath 提供

Problem 2

Three identical rectangles are put together to form rectangle ABCD, as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is 5 feet, what is the area in square feet of rectangle ABCD?

三个相同的矩形组合在一起形成了矩形ABCD，如下图所示。已知每个小矩形的较短边的长度为5英尺，矩形ABCD的面积是多少平方英尺？

(A) 45 (B) 75 (C) 100 (D) 125 (E) 150

Solutions