2012 AMC 12A 第 6 题

Question

三个整数两两相加的和分别为

12

、

17

和

19

。中间的那个数是多少？

The sums of three whole numbers taken in pairs are

12,

17,

and

19.

What is the middle number?

4

5

6

7

8

知识点：方程组

把三个两两之和相加，会把每个数都数两次

Adding all three pairwise sums counts each number twice

总和

a+b+c

是

12+17+19

的一半；用总和减去每个两数之和即可得到第三个数

The total

a+b+c

is half of

12+17+19

; subtract each pair sum to get the third number

设三个数为

a \lt b \lt c

。将三个两两之和相加，得到

2(a+b+c) = 12+17+19

= 48

，所以

a+b+c = 24

。

因此

a = 24-19 = 5

，

b = 24-17 = 7

，

c = 24-12 = 12

。中间的数是

7

。

因此，正确答案是 D。

Let the numbers be

a \lt b \lt c.

Adding the three pairwise sums gives

2(a+b+c) = 12+17+19

= 48,

so

a+b+c = 24.

Then

a = 24-19 = 5,

b = 24-17 = 7,

and

c = 24-12 = 12.

The middle number is

7.

Thus, the correct answer is D.

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