Question: In Atlanta, the tax on a property assessed at $960,000$ is $15,360$. Which of the following proportions could you use to find the tax on a property assessed at $820,000$? Select ALL proportions that could work.
\frac{15360}{820000} = \frac{960000}{x}
\frac{820000}{x} = \frac{960000}{15360}
\frac{x}{15360} = \frac{820000}{960000}
\frac{15360}{960000} = \frac{x}{820000}
1. **State the problem:** We know the tax on a property assessed at $960,000$ is $15,360$. We want to find the tax $x$ on a property assessed at $820,000$ using proportions.
2. **Formula for proportionality:** The tax is proportional to the assessed value, so we use the proportion:
$$\frac{\text{tax}_1}{\text{value}_1} = \frac{\text{tax}_2}{\text{value}_2}$$
or
$$\frac{15,360}{960,000} = \frac{x}{820,000}$$
3. **Check each given proportion:**
- Option 1: $$\frac{15360}{820000} = \frac{960000}{x}$$
Cross-multiplied: $$15360 \times x = 820000 \times 960000$$
This does not match the correct setup because the known tax $15360$ should be paired with $960000$, not $820000$. So this proportion is **incorrect**.
- Option 2: $$\frac{820000}{x} = \frac{960000}{15360}$$
Cross-multiplied: $$820000 \times 15360 = 960000 \times x$$
Rearranged: $$x = \frac{820000 \times 15360}{960000}$$
This matches the correct proportional relationship, so this proportion is **correct**.
- Option 3: $$\frac{x}{15360} = \frac{820000}{960000}$$
Cross-multiplied: $$x \times 960000 = 15360 \times 820000$$
Rearranged: $$x = \frac{15360 \times 820000}{960000}$$
This matches the correct proportional relationship, so this proportion is **correct**.
- Option 4: $$\frac{15360}{960000} = \frac{x}{820000}$$
This is exactly the original proportion we started with, so this proportion is **correct**.
4. **Summary:** The correct proportions are options 2, 3, and 4.
5. **Final answer:**
$$\boxed{\text{Options 2, 3, and 4 are correct proportions to find } x}$$