Question

三个三角形和一个菱形与九个圆点平衡。另外，一个三角形与一个菱形和一个圆点平衡。两个菱形需要多少个圆点来平衡？

Three triangles and a diamond balance nine dots. Also, one triangle balances a diamond and a dot. How many dots will balance two diamonds?

$1$

$2$

$3$

$4$

$5$

设一个三角形重 $t$ ，一个菱形重 $d$ ，一个圆点重 $1$ ，把两个平衡条件写成方程

Let a triangle weigh $t$ , a diamond $d$ , and a dot $1$ ; write the two balance conditions as equations

由 $t = d + 1$ 和 $3t + d = 9$ 代入求出 $d$ ，再把它加倍

From $t = d + 1$ and $3t + d = 9$ , substitute to solve for $d$ , then double it

设三角形、菱形和圆点的重量分别为 $t$ 、 $d$ 和 $1$ 。题意给出 $3t + d = 9$ 和 $t = d + 1$ 。

代入得 $3(d+1) + d = 9$ ，所以 $4d + 3 = 9$ ， $d = \dfrac32$ 。两个菱形重 $2d = 3$ 个圆点。

所以正确答案是 C。

Let a triangle, diamond, and dot weigh $t$ , $d$ , and $1$ . The conditions give $3t + d = 9$ and $t = d + 1$ .

Substituting, $3(d+1) + d = 9$ , so $4d + 3 = 9$ and $d = \dfrac32$ . Then two diamonds weigh $2d = 3$ dots.

Thus, the correct answer is C .