The amount of taxes a city collect is proportional to the population of the city. If the city...

Question:

The amount of taxes a city collect is proportional to the population of the city.

If the city collects $6 billion in 1982 when the population was 2 million people, how much did the city collect in 1990 when the population was 3 million people?

Proportionality

When the amount of one quantity is proportional to another quantity, we can write a statement relating them. This statement involves some constant of proportionality, k.

{eq}y = kx {/eq}

Answer and Explanation:

Since the amount of tax collected is proportional to the population, we can construct a statement relating these quantities through a constant of proportionality, k.

{eq}T = kp {/eq}


Since we know that $6 billion in taxes were collected when the population was 2 million people, we can find this constant of proportionality as follows.

{eq}6000000000 = k(2000000)\\ k = \frac{6000000000}{2000000} = 3000 {/eq}


Thus, we can use this to find the amount of tax collected when the population is 3 million people.

{eq}T = 3000(3000000) = 9000000000 {/eq}


Therefore, $9 billion in taxes were collected in 1990 when the population was 3 million people.


Learn more about this topic:

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Identifying the Constant of Proportionality

from 6th-8th Grade Math: Practice & Review

Chapter 50 / Lesson 13
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