# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Tue, 6 Dec 2016 09:13:20 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 3 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: Matrix MultiplicationsPosted: Sun, 10 Aug 2008 17:08:49 UTC
 S.O.S. Newbie

Joined: Sun, 10 Aug 2008 16:42:43 UTC
Posts: 2
I have a question about the problem below:

Consider a city with two kinds of population: the inner city population and the suburb population. We assume that every year 40% of the inner city population moves to the suburbs, while 30% of the suburb population moves to the inner part of the city. Let I (resp. S) be the initial population of the inner city (resp. the suburban area). So after one year, the population of the inner part is

0.6 I + 0.3 S

My questions are as follows:

(1) How did they arrive at 0.6 I + 0.3 S ?

(2) What does "I (resp. S)" and "(resp. the suburban area)" stand for ?

Top

 Post subject: Re: Matrix MultiplicationsPosted: Sun, 10 Aug 2008 20:27:03 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sat, 7 Jan 2006 18:29:24 UTC
Posts: 1401
Location: Leeds, UK
definite variables wrote:
I have a question about the problem below:

Consider a city with two kinds of population: the inner city population and the suburb population. We assume that every year 40% of the inner city population moves to the suburbs, while 30% of the suburb population moves to the inner part of the city. Let I (resp. S) be the initial population of the inner city (resp. the suburban area). So after one year, the population of the inner part is

0.6 I + 0.3 S

My questions are as follows:

(1) How did they arrive at 0.6 I + 0.3 S ?

(2) What does "I (resp. S)" and "(resp. the suburban area)" stand for ?

To answer the second part first, "resp." means "respectively". In other words, the sentence containing that abbreviation is a shorthand way of saying "Let I be the initial population of the inner city and let S be the initial population of the suburban area."

Notice that 40% = 0.4, and 30% = 0.3. If, out of an initial population of I, an amount given by 0.4 I leave the inner city then only 0.6 I remain. But we have to add to that the 0.3 S that move in from the suburbs. That's where the expression 0.6 I + 0.3 S comes from.

Top

 Post subject: Re: Matrix MultiplicationsPosted: Mon, 11 Aug 2008 13:38:57 UTC
 S.O.S. Newbie

Joined: Sun, 10 Aug 2008 16:42:43 UTC
Posts: 2
Opalg wrote:
definite variables wrote:
I have a question about the problem below:

Consider a city with two kinds of population: the inner city population and the suburb population. We assume that every year 40% of the inner city population moves to the suburbs, while 30% of the suburb population moves to the inner part of the city. Let I (resp. S) be the initial population of the inner city (resp. the suburban area). So after one year, the population of the inner part is

0.6 I + 0.3 S

My questions are as follows:

(1) How did they arrive at 0.6 I + 0.3 S ?

(2) What does "I (resp. S)" and "(resp. the suburban area)" stand for ?

To answer the second part first, "resp." means "respectively". In other words, the sentence containing that abbreviation is a shorthand way of saying "Let I be the initial population of the inner city and let S be the initial population of the suburban area."

Notice that 40% = 0.4, and 30% = 0.3. If, out of an initial population of I, an amount given by 0.4 I leave the inner city then only 0.6 I remain. But we have to add to that the 0.3 S that move in from the suburbs. That's where the expression 0.6 I + 0.3 S comes from.

Awesome!

Thanks.

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 3 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix and Linear Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous