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rvca

rvca

Member
This is an 8th grade math problem (for my lil sis' class) I spent like 5 minutes on it and had some trouble. I got an answer but i dont think its right. So I look to NS to help answer my sisters math problem...

The plan is for each individual who can read to spend one year teaching two others to read. After one year that teacher is done but the two new readers must spend one year, each teaching two others to read. If 1000 people can read at the start, how many people will be able to read in ten years?

My answer was 1,277,000 people. But i have a bad feeling about it. A confirmation on that answer or a new one with a good reason would be greatly appreciated... Thanks NS!
 
1000-----2000-----4000-8000----16000----32000----64000--128000---256000----512000
im scared of sounding like a retard by posting this but doesnt it make sense that it just doubles every year
 
that was my first thought process, but then i remembered that after the first thousand people teach two more, they are done and dont teach anymore people
 
ya so 1000 people teach 2 people each so now 2000 people can read then 2000 people teach 2 each so now 4000 can read and so on
 
i think you are all wrong right from the start.

1000 people start knowing how to read. then each of them teaches 2 people to read, so then 3000 people now know how to read, not just 2000.
 
its not that simple though. think about it in smaller numbers like 1 instead of a thousand. if you have one person teach two people, at the end of that year you have three people who can read
 
ya but that doesnt change much i dont think

1000 people can read they teach 2 each so now 3000 people can read in total but the original 1000 arent teaching anybody anymore so only the 2000 teachers teach 2 people which bring it to 4000 or 6000 but the 2000 who taugh the 4000 dont teach anymore so only 8000 people read i guess u can just add 1000 to the final anwser if you want but im pretty sure it just doubles every year
its grade 8 here guys there not trying to trick anyone
 
ahh yeah, i missed that aprt in the problem that they stop teaching. so my answer was very wrong. this is a good problem.
 
i know what you're saying but the question asks for the total amount of people that can read at the end of the 10 years. not just the new readers
 


year0

year1

year2

year3

year4

year5

year6

year7

year8

year9

year10

teachers

1000

2000

4000

8000

16000

32000

64000

128000

256000

512000

1024000

readers

2000

4000

8000

16000

32000

64000

128000

256000

512000

1024000

2048000

sum

4095000

i did the sum of the teacher plus the amount of readers in year ten
 
you need to make sure the teachers who just taught don't get counted in how many new people get taught per year but than you have to add up all the original teachers at the start of each year who didn't taught but still know how to read.
 
this is the way i see it (I really dont know if its right, im just goin with it)

you get this function:

# of people who know how to read = 1000x + 1000

x being the amount of years after this whole chain starts

i dunno if it works but i tested it for the first 2 years and it seems to work...
 
that doesnt work
it goes 1000---2000----4000 so 7000 after 3 years which is right
and your equation goes
1000.1+1000=20001000.2+1000=30001000.3+1000=40001000.4+1000=5000
 
ok, dont know why but i felt compelled to sit down and figure this out,

in a simpler form,

1+2 = 3

2+4 = 6

4+8 = 12

8+16= 24

ect. adding up the numbers on the right because the people teach two others but are done after that the next year only the people who learned teach. and multiply by 1000 at the end.

for a total of 3069000

check my work though i did most in my head
 
maybe

what did you get?

i did it in 1's then multiplied by 1000

people not teaching I people teaching I people that can read

0 1 3

1 2 7

3 4 15

7 8 16+8+7=31

15 16 16(2)=32+16+15=63

21 32 32(2)-64+21+32=117

53 64 128+53=181

117 64 128+117=245

181 64 128+181=309

245 64 128+245=373

373 X 1000 = 373,000

i think i may have messed up somewhere along the line. i feel like there should be a rule to this.

 
i though about it some more and there are no readers in year ten. this this the correct answer

year0

year1

year2

year3

year4

year5

teachers

1000

2000

4000

8000

16000

32000

readers

2000

4000

8000

16000

32000

64000

year6

year7

year8

year9

year10

teachers

64000

128000

256000

512000

1024000

readers

128000

256000

512000

1024000

2047000

 
i think he's got it right. i restarted and thats the same method i was using for the first couple years and i got the same answers. it makes sense.
 
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