AMC 8 2022 Problem 13
AMC8 2022 年第 13 题
特殊数与不定方程★★★☆☆
How many positive integers can fill the blank in the sentence below? “One positive integer is _____ more than twice another, and the sum of the two numbers is 28 .”
有多少个正整数可以填在下面句子的横线上？
“一个正整数是另一个的两倍加上，并且这两个数的和是 28”。
- A.6
- B.7
- C.8
- D.9
- E.10
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
Let and be positive integers such that m>n and m+n=28. It follows that m=2n+d for some positive integer $d.$ We wish to find the number of possible values for $d.$ By substitution, we have (2n+d)+n=28, from which d=28-3n. Note that each generate a positive integer for $d,$ so there are 9 possible values for $d.$
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