To find the tax on a property assessed at \[tex]$600,000 given that the tax on a property assessed at \$[/tex]940,000 is \[tex]$13,160, we can set up proportions using the relationship between the assessed value and the tax.
### Step-by-Step Solution:
1. Identify the known ratio:
The known ratio is:
\[
\frac{\text{Tax}}{\text{Assessed Value}} = \frac{13160}{940000}
\]
2. Set up the proportion for a property assessed at \$[/tex]600,000:
Let [tex]\( x \)[/tex] be the tax on the property assessed at \$600,000. We need to find the proportions that relate the taxes and assessed values correctly.
3. Evaluate each given proportion:
- First proportion:
[tex]\[
\frac{600000}{x} = \frac{940000}{13160}
\][/tex]
Cross-multiplying gives:
[tex]\[
600000 \times 13160 = 940000 \times x \implies x = \frac{600000 \times 13160}{940000}
\][/tex]
This proportion correctly sets up the relationship between the values, so it is valid.
- Second proportion:
[tex]\[
\frac{13160}{940000} = \frac{x}{600000}
\][/tex]
Cross-multiplying gives:
[tex]\[
13160 \times 600000 = 940000 \times x \implies x = \frac{13160 \times 600000}{940000}
\][/tex]
This proportion correctly sets up the relationship between the values, so it is valid.
- Third proportion:
[tex]\[
\frac{13160}{600000} = \frac{940000}{x}
\][/tex]
Cross-multiplying gives:
[tex]\[
13160 \times x = 600000 \times 940000 \implies x = \frac{600000 \times 940000}{13160}
\][/tex]
Upon inspection, this proportion incorrectly sets up the relationship between the values. It would solve for an incorrect value, so it is not valid.
- Fourth proportion:
[tex]\[
\frac{x}{13160} = \frac{600000}{940000}
\][/tex]
Cross-multiplying gives:
[tex]\[
x \times 940000 = 600000 \times 13160 \implies x = \frac{600000 \times 13160}{940000}
\][/tex]
This proportion correctly sets up the relationship between the values, so it is valid.
### Conclusion:
The correct proportions are:
[tex]\[
\boxed{\frac{600000}{x} = \frac{940000}{13160}, \ \frac{13160}{940000} = \frac{x}{600000}, \ \frac{x}{13160} = \frac{600000}{940000}}
\][/tex]
