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
Vivian L.
02/09/14