AMC8 1990

AMC8 1990 · Q24

AMC8 1990 · Q24. It mainly tests Linear equations.

Three $\triangle$ and a $\diamond$ will balance nine $\bullet$'s. One $\triangle$ will balance a $\diamond$ and a $\bullet$. How many $\bullet$'s will balance the two $\diamond$'s in this balance?

三个 $\triangle$ 和一个 $\diamond$ 可以平衡九个 $\bullet$。一个 $\triangle$ 可以平衡一个 $\diamond$ 和一个 $\bullet$。在这个天平中，两个 $\diamond$ 可以平衡多少个 $\bullet$？

(A) 1 1

(B) 2 2

(D) 4 4

(E) 5 5

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): The second balance shows each $\triangle$ balances $\diamond\bullet$. Replace each $\triangle$ on the first balance with $\diamond\bullet$. Then after removing three $\bullet$'s from each side, the balance has $\diamond\diamond\diamond\diamond\diamond$ on the left and $\bullet\bullet\bullet\bullet\bullet$ on the right. Thus $\diamond\diamond$ will be balanced by $\bullet\bullet\bullet$.

答案（C）：第二个天平表明每个 $\triangle$ 与 $\diamond\bullet$ 平衡。将第一个天平上的每个 $\triangle$ 都替换为 $\diamond\bullet$。然后从天平两边各去掉三个 $\bullet$，天平左边剩下 $\diamond\diamond\diamond\diamond\diamond$，右边剩下 $\bullet\bullet\bullet\bullet\bullet$。因此，$\diamond\diamond$ 与 $\bullet\bullet\bullet$ 平衡。

Topics

AL.001 Linear equations