need step by step instruction about how to solve this problem

Question

from 1900 to 2000, the population rate of seattle washington grew at a rate of about 4700 people to a population of about 565,000. Baltimore maryland decreased at a rate of about 8400 people per year to a population of about 650000. If these rates continue in about how many years will seattle and baltimore have the same population

Answer 1

Seattle increases at a rate of 4700 people per year.

Baltimore decreases at a rate of 8400 people per year.

let x= # of years until the populations are the same

565,000+4700x=650,000-8400x

4700x+8400x=650,000-565,000

13,100x=85,000

x=85,000/13,100

x=6.488549 years or about 6.5 years

Answer 2

Hi Jen;

I assume "4700 people" is 4700 people/year.

I also assume this is a ten year period of 1990-2000, not 100 years from 1900-2000.  Please correct me if I am wrong.

S=initial population of Seattle

S+[(4,700 people/year)(10 years)]=565,000 people

Let's solve...

Let's note the fact that the unit of year is in both the denominator and numerator.  It cancels...

S+[(4,700 people/year)(10 years)]=565,000 people

S+[(4,700 people)(10)]=565,000 people

The only unit remaining is people.  This is what we want.

S+47,000 people=565,000 people

Let's subtract 47,000 from both sides...

S+47,000-47,000=565,000-47,000

S=518,000

 

B=initial population of Baltimore

B-[(8,400 people/year)(10 years)=650,000 people

B-[(8,400 people/year)(10 years)=650,000 people

B-[(8,400 people)(10)]=650,000 people

B-84,000 people=650,000 people

B-84,000 people+84,000 people=650,000 people + 84,000 people

B=734,000

 

x=quantity of years for both populations to be equal...

(518,000 people)+[(4,700 people/year)(x years)]=(734,000 people)-[(8,400 people/year)(x years)]

The unit of years is in the numerator and denominator of the bracketed equations.  It cancels...

(518,000 people)+[(4,700 people/year)(x years)]=(734,000 people)-[(8,400 people/year)(x years)]

(518,000 people)+[(4,700 people)(x)]=(734,000 people)-[(8,400 people)(x)]

The unit of people is in the numerator of all facets of the equation.  It cancels...

(518,000 people)+[(4,700 people)(x)]=(734,000 people)-[(8,400 people)(x)]

(518,000)+[4,700(x)]=(734,000)-[8,400(x)]

Let's subtract 518,000 from both sides...

4,700(x)=216,000-[8,400(x)]

Let's add 8,400(x) to both sides...

13,100x=216,000

Let's divide both sides by 13,100...

x=16 years

 

Answer 3

It was a mistake. So it has to be done over.

 

S -- population of Seattle in 1900

 

     S + 4700 ( 10 ) = 565000

     S = 565,000 - 47,000 = 518,000

 

B -- Population of Baltimore in 1900.

 

        B - 8400(10) = 650,000

        B = 65,000 + 84,000 = 734,000

 

   734, 000 -n ( 8400) = 518,000 + n ( 4700)

   

    734,000 - 518,000 = n ( 4700 + 8400)

 

           216, 000 = n ( 13,100)

    

          n = 216,000 / 13, 100 = 16.5∼ 17

         In Year 1917, both population becomes equal.

 

       

Answer 4

Seattle: (year 2000, 565000 people), m = 4700 people/year

 

Using point-slope form:

 

S - 565000 = 4700)(t - 2000)

 

S = 4700(t - 2000) + 565000

 

Baltimore: (2000, 650000), m = -8400

 

B - 650000 = -8400(t - 2000)

 

B = -8400(t - 2000) + 650000

 

When same?

 

S = B

 

  4700(t-2000)+565000 = -8400(t-2000)+650000

+8400(t-2000)-565000 = +8400(t-2000)-565000

13100(t-2000) + 0 = 0 + 85000

 

t-2000 = 85000/13100 = 850/131

 

t = 850/131+2000 = 850/131+131*2000/131 = 262850/131

 

t ≈ 2006.48854961832061

 

By this model the populations were the same at 5:46:16 PM on May 26, 2006.