Question

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

$1$

$2$

$3$

$4$

$5$

Difficulty rating: 1120

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 .