Math Help Fast!!

[Danielkang2]

I know the math behind it but don't understand the problem. I need the answer fast as I'm going to sleep in a little bit. Here's the problem

A region's population density is the number of people per square mile. The tiny country of Monaco has the highest population density in the world, with 33,000 people living in an area of 0.75 square mile. The state of New York has a population of about 19,000,000 people living in an area of about 47,000 square miles. Use a calculator to complete the following. Round your answers to the nearest whole number.

a. Write and solve a proportion to find how many people would live in Monaco if Monaco had the population density of New York.
b. Write and solve a proportion to find how many people would live in New York if New York had the population density of Monaco.

 

[EpicGamer12]

Just set up a ratio and cross multiply.

 

[Danielkang2]

Yeah, but that's the part I didn't understand. Is 33,000 over .75 a ratio and 19,000,000 over 47,000 the other ratio? I can do the math but I don't know how to set up this word problem into a equation.

 

[KarlaKGB]

This problem is best tackled by working with actual population densities aka people per square mile.

a. First, calculate New York's population density (how many people live in one square mile in New York). Then use that to calculate how many people would live in 0.75 square miles.

b. Again calculate Monaco's population density. Then use that to calculate how many people would live in 47,000 square miles.

It seems you don't understand what the question is asking for. 33000 over 0.75 is one ratio, and 19000000 over 47000 is another ratio, but the two have nothing to do with each other. You use one ratio in one question, and the other ratio in the other question. But do you understand which ratio to use in which question? My explanations for a. and b. above should make it clear to you which ratio to use.

 

[Danielkang2]

I got this. a. 17,787,234 people
b. 2,068,000,000 people
I don't know how to write the proportion. :O

- - - Post Merge - - -

Math is my worst subject.

 

[KarlaKGB]

a. is wrong

b. is correct

You can easily see a. is wrong if you do a sanity check on your answer. Think about it. You have 19,000,000 people living in 47,000 square miles. If Monaco is less than 1 square mile, how can you still have 17,787,234 people living there?

For question a, I'm going to take you through the thinking. When you work with proportions and ratios, what you're essentially doing is scaling.

In question a, it's asking you to find how many people would live in Monaco if it had the same population density as NY. Well first you have to work out the population density of NY, which is your proportion.

Write it as the fraction 19000000/47000. That's 19,000,000 people per 47,000 square miles. Now the question asks you to find out how many people would live in Monaco. You write another fraction, x / 0.75. x is the number of people, which you're trying to work out. 0.75 is the area of Monaco, which you do know. And because you're scaling, the two proportions are equal to each other.
So,
19000000/47000 = x / 0.75

Now you just solve for x, which I hope you know how to do.

---
The other way to think about it (which is mathematically identical) is...

if there are 19,000,000 people per 47,000 square miles, then there are 19000000/47000 (=404) people per square mile. And if there are 404 people per square mile, then there would be 404 * 0.75 (=303) people in 0.75 square miles. Understand?

 

[Danielkang2]

a. is wrong

b. is correct

You can easily see a. is wrong if you do a sanity check on your answer. Think about it. You have 19,000,000 people living in 47,000 square miles. If Monaco is less than 1 square mile, how can you still have 17,787,234 people living there?

For question a, I'm going to take you through the thinking. When you work with proportions and ratios, what you're essentially doing is scaling.

In question a, it's asking you to find how many people would live in Monaco if it had the same population density as NY. Well first you have to work out the population density of NY, which is your proportion.

Write it as the fraction 19000000/47000. That's 19,000,000 people per 47,000 square miles. Now the question asks you to find out how many people would live in Monaco. You write another fraction, x / 0.75. x is the number of people, which you're trying to work out. 0.75 is the area of Monaco, which you do know. And because you're scaling, the two proportions are equal to each other.
So,
19000000/47000 = x / 0.75

Now you just solve for x, which I hope you know how to do.

---
The other way to think about it (which is mathematically identical) is...

if there are 19,000,000 people per 47,000 square miles, then there are 19000000/47000 (=404) people per square mile. And if there are 404 people per square mile, then there would be 404 * 0.75 (=303) people in 0.75 square miles. Understand?

Thank You so much I actually had 303 for a but I overthought it and changed my answer. Thank You!