Question

三个非负整数两两相加得到的和分别为 $12, 17$ 和 $19$ 。这三个数中的中间那个数是多少？

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

设三个数为 $a, b, c$ ，且 $a \lt b \lt c$ 。由于三个和都不同，所以这三个数也互不相等。

题意给出以及 $a + b = 12, a + c = 17,$ $b + c = 19.$

把三式相加，得到 $2(a + b + c) = 48.$

因此再减去得到 $b = 7$ 。 $a + b + c = 24,$ $a + c = 17,$

所以正确答案是 D。

Let the three numbers be $a, b, c$ where $a \lt b \lt c.$ None of them are equal, since all three sums are different.

Then $a + b = 12, a + c = 17,$ and $b + c = 19.$

Adding all three equations together gives us $2(a + b + c) = 48.$

Then $a + b + c = 24,$ from which we can subtract $a + c = 17,$ to get $b = 7.$

Thus, D is the correct answer.