The land of Catania uses gold coins and silver coins. Gold coins are 1mm thick and silver coins are 3 mm thick. In how many ways can Taylor make a stack of coins that is 6 mm tall using any arrangement of gold and silver coins, assuming order matters ?
A. 4
B. 5
C. 6
D. 7
E. 8

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Worked solution

1. 2026 AMC 8 官方解析

设有 $x$ 枚金币， $y$ 枚银币
$x + 3y = 6$
$\begin{cases} x = 6 \\ y = 0 \end{cases} \quad \begin{cases} x = 3 \\ y = 1 \end{cases} \quad \begin{cases} x = 0 \\ y = 2 \end{cases}$
1种 $\quad$ 4种 $\quad$ 1种 $\quad$ 共6种 .

Answer

C. 6

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The land of Catania uses gold coins and silver coins. Gold coins are 1mm thick and silver coins are 3 mm thick. In how many ways can Taylor make a stack of coins that is 6 mm tall using any arrangement of gold and silver coins, assuming order matters ?A. 4B. 5C. 6D. 7E. 8

Worked solution

More questions on this topic

The land of Catania uses gold coins and silver coins. Gold coins are 1mm thick and silver coins are 3 mm thick. In how many ways can Taylor make a stack of coins that is 6 mm tall using any arrangement of gold and silver coins, assuming order matters ?
A. 4
B. 5
C. 6
D. 7
E. 8