If $2$ equal parts of zinc together weigh $z$ kilograms, what is the weight of just $1$ of those parts?

Once you know the weight of $1$ part, multiply it by the number of parts that represent copper in the ratio to get the total copper.

In Desmos, create a slider by typing z = 10 (or any positive number) and pressing enter. This will represent $z$ kilograms of zinc.

For each option, type the corresponding expression for copper in terms of $z$, for example c_A = (2/3)*z, c_B = (3/2)*z, c_C = z - 1, c_D = 3*z. Desmos will show the copper amount for your chosen value of $z$.

For each expression, type the ratio c_A / z, c_B / z, etc. The correct expression is the one where this ratio equals $3/2$, matching the copper to zinc ratio of $3$ to $2$ given in the problem.

The ratio of copper to zinc is $3$ to $2$. This means:

• Copper is divided into $3$ equal parts.
• Zinc is divided into $2$ equal parts. So, for every $3$ parts of copper, there are $2$ parts of zinc.

We are told the alloy contains $z$ kilograms of zinc.

In the ratio, zinc corresponds to $2$ parts. So:

• $2$ parts of zinc $=$ $z$ kilograms.
• Therefore, $1$ part of zinc (and of the alloy in general) must be $\dfrac{z}{2}$ kilograms.

Copper corresponds to $3$ parts in the ratio.

If each part is $\dfrac{z}{2}$ kilograms, then the amount of copper is:

So the expression that represents the number of kilograms of copper is $\dfrac{3}{2}z$.