Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Percent Change of Gross Domestic Product

The population of City X increased from 2 million in the year 2000 to 2.5 million in 2015 and the gross domestic product of the city in 2000 was 3/8 less than that in 2015. What was the approximate percent change, rounded to the nearest integer if required, in the per capita gross domestic product of the city from 2000 to 2015?

My set up:

Population in 2015 minus population in 2000 divided by original population in 2000 equals percent P divided by 100.

(2.5 - 2)/(2,000) = P/100

Is this correct?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Percent Change of Gross Domestic Product

What happened to call the unknown x ?

I would tackle this like this.

Call the GDP in 2015 x.

Then in 2000 it is 5x/8

GDP per capita is 5x/8 divided by 2millon
and x divided by 2.5million

From those work out the percentage change.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Percent Change of Gross Domestic Product

What happened to call the unknown x ?

I would tackle this like this.

Call the GDP in 2015 x.

Then in 2000 it is 5x/8

GDP per capita is 5x/8 divided by 2millon
and x divided by 2.5million

From those work out the percentage change.

Bob

Where did 5/8 come from?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Percent Change of Gross Domestic Product

I think I'm reading this correctly.   If an item is reduced by 20% then the amount you have to pay is 80% of the old price.

We're told the old GDP is 3/8 less so I interpreted that as meaning 5/8 of the other GDP.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Percent Change of Gross Domestic Product

I think I'm reading this correctly.   If an item is reduced by 20% then the amount you have to pay is 80% of the old price.

We're told the old GDP is 3/8 less so I interpreted that as meaning 5/8 of the other GDP.

Bob

You said:

"GDP per capita is 5x/8 divided by 2millon
and x divided by 2.5million."

(5x/8)/(2,000,000) = x/(2,500,000)

Correct?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Percent Change of Gross Domestic Product

Not quite. The two calculations are good for the per capita GDPs.  But don't set them equal.

The question asks for the percentage change.

That is change over what it was (in 2000) times by 100 to make it a percentage.

You should find all the xs cancel out so it doesn't matter that we don't know what x is. This time the answer isn't to find x.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Percent Change of Gross Domestic Product

Not quite. The two calculations are good for the per capita GDPs.  But don't set them equal.

The question asks for the percentage change.

That is change over what it was (in 2000) times by 100 to make it a percentage.

You should find all the xs cancel out so it doesn't matter that we don't know what x is. This time the answer isn't to find x.

Bob

Can you please set it up for me?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Percent Change of Gross Domestic Product

2000 figure is (5x/8)/(2,000,000)

2015 figure is x/(2,500,000)

Percentage change is found by

It's worth cancelling out the xs and the millions next.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Percent Change of Gross Domestic Product

2000 figure is (5x/8)/(2,000,000)

2015 figure is x/(2,500,000)

Percentage change is found by

It's worth cancelling out the xs and the millions next.

Bob

Very good, Bob. I will surely take it from here. Like I said before, this site is perfect for word problems. However, I would like to see more participants.