Question

The tax on a property with an assessed value of $70,000 is $1,100. What is the assessed value of a property in the same district, if the tax on that property is $1,400?

Answer 1

They've given me two categories of things: assessed values of properties, and the amounts of taxes paid. My ratios will then use these two categories. I will set up my ratios with the assessed valuation on top (because that's what I read first in the exercise), and I will use "v" to stand for the value that I need to find.

value
tax
:
70,000
1,100
=
v
1,400
tax
value
​
:
1,100
70,000
​
=
1,400
v
​

I'll use the shortcut method for solving, multiplying the 70,000 and the 1,400 in one direction, and then dividing by the 1,100 going in the other direction:

70,000 / 1,100 = v / 1,400; multiplying gives (70,000)(1,400); dividing gives v = [(70,000)(1,400)]/1,100
v
=
(
70,000
)
(
1,400
)
1,100
v=
1,100
(70,000)(1,400)
​

v
=
98,000,000
1,100
v=
1,100
98,000,000
​

v
=
89,090.9090909...
v=89,090.9090909...
Since the solution is a dollars-and-cents value, I must round the final answer to two decimal places; the "exact" form (whether repeating decimal or fraction) wouldn't make sense in this context. So my answer is: $ 89.090.91