2021年必威体育精装版美国数学竞赛 AMC 10A （解析版）.pdf

批注[c1]: 2021 AMC 10A Problem 1 What is the value of Solution 1 This corresponds to Problem 2 Portias high school has times as many students as Laras high school. The two high schools have a total of students. How many students does Portias high school have? Solution 1 The following system of equations can be formed with representing the number of students in Portias high school and representing the number of students in Laras high school. Substituting with we get . Solving for , we get . Since we need to find we multiply by 3 to get , which is Problem 3 The sum of two natural numbers is . One of the two numbers is divisible by . If the units digit of that number is erased, the other number is obtained. What is the difference of these two numbers? Solution 1 The units digit of a multiple of will always be . We add a whenever we multiply by . So, removing the units digit is equal to dividing by . Let the smaller number (the one we get after removing the units digit) be . This means the bigger number would be . 1 / 16 We know the sum is so . So . The difference is . So, the answer is . Problem 4 A cart rolls down a hill, travelling inches the first second and accelerating so that during each successive -second time interval, it travels inches more than during the previous -second interval. The cart takes seconds to reach the bottom of the hill. How far, in inches, does it travel? Solution 1 (Arithmetic Series) Since we seek the sum