Solving a Population Growth Problem

[math2014]

Ok so this is homework question, i know it is supposed to be here but the math question would not go in any homewrok category i need help and my parents do not even know how to solve it. Math question:




The population of Heidi's hometown is 18,079 people in 2006. In 2007 it was 19,087 people. During 2008 the towns population grew by an amount that was a multiple of 9. The population was less than 20,000 people and used the five digits 1,9,0,8, and 7. What could have been the population at the end of 2008? Can you find all possible answers? Explain how you know.



READ THE PROBLEM CAREFULLY. Also remember the population grew, not decreased. Please help me.


I have divided and did everything to get the population. There is no possible population if you agree say you agree if not tell me what i did wrong.

 

[BOAS]

Ok so this is homework question, i know it is supposed to be here but the math question would not go in any homewrok category i need help and my parents do not even know how to solve it. Math question:




The population of Heidi's hometown is 18,079 people in 2006. In 2007 it was 19,087 people. During 2008 the towns population grew by an amount that was a multiple of 9. The population was less than 20,000 people and used the five digits 1,9,0,8, and 7. What could have been the population at the end of 2008? Can you find all possible answers? Explain how you know.



READ THE PROBLEM CAREFULLY. Also remember the population grew, not decreased. Please help me.


I have divided and did everything to get the population. There is no possible population if you agree say you agree if not tell me what i did wrong.

I can see four possible values for the population.

If you outline specifically what you did, I can help.

But it is the policy here that you must show your working up until the point you became stuck,

 

[haruspex]

If two numbers consist of the same digits, just in a different order, what can you say about factors of the difference of the two numbers?

 

[math2014]

I can see four possible values for the population.

If you outline specifically what you did, I can help.

But it is the policy here that you must show your working up until the point you became stuck,

I divided 19,708 , 19,807 , 19,780 , and 19870 by nine but none were divisible

 

[haruspex]

I divided 19,708 , 19,807 , 19,780 , and 19870 by nine but none were divisible

Read the question again:

grew by an amount that was a multiple of 9

 

[math2014]

Just tell me the answer

 

[haruspex]

Just tell me the answer

No, that's not how these forums work.
Don't expect the answers to this question to be numbers that are divisible by 9. It says the population "grew by" a number that's divisible by 9. It does not say "grew to" a number that's divisible by 9.

18,079 people in 2006. In 2007 it was 19,087 people

How much did the population grow by in that case? Is that number divisible by 9? How might you have realized whether it would be divisible by 9 without even calculating the number?

Spoiler

Take any number, any number of digits. Make another number by shuffling the digits around. Subtract the one from other. Is the result divisible by 9?