Problem, i went wrong somewhere

[Trail_Builder]

im stuck on this problem, which is annoying because it looks straightforward, i think i just made a clanger somewhere and can't find where lol, hope you can help... thnx

Homework Statement

Five clever newsboys formed a partnership and disposed of their papers in the following manner. Tom Smith sold one paper more than one quarter of the whole lot, Billy Jones disposed of one paper more than a quarter of the remainder, Ned Smith sold one paper more than a quarter of what was left, and Charley Jones disposed of one paper more than a quarter of the remainder. At this stage, the Smith boys had together sold just one hundred papers more than the Jones boys had sold. Little Jimmy Jones, the youngest kid in the bunch, now sold all the papers that were left.

The three Jones boys sold more papers than the two Smith boys, but how many more?

2. Notation

Tom Smith = T
Billy Jones = B
Ned Smith = N
Charley Jones = C
Jimmy Jones = J

Total number of papers = t

The Attempt at a Solution

What I gathered from the problem statement.

T = 1/4t + 1
B = 3/16t
N = 9/64t
C = 27/256t
T + N - 100 = B + C
J = 81/256t - 1

From that I substituted the letters into T + N - 100 = B + C

T + N - 100 = B + C
1/4t + 1 + 9/64t - 100 = 3/16t + 27/256t
1/4t + 9/64t - 99 = 3/16t + 27/256t
25/64t - 99 = 75/256t
25/64t = 75/256t + 99
25/256t = 99
t = 1013 19/25 ??

there can't be a non integer as the no of papers?

im confused, i think i went wrong at some poitn but can't find where, can anyone help? thnx

 

[HallsofIvy]

im stuck on this problem, which is annoying because it looks straightforward, i think i just made a clanger somewhere and can't find where lol, hope you can help... thnx

Homework Statement

Five clever newsboys formed a partnership and disposed of their papers in the following manner. Tom Smith sold one paper more than one quarter of the whole lot, Billy Jones disposed of one paper more than a quarter of the remainder, Ned Smith sold one paper more than a quarter of what was left, and Charley Jones disposed of one paper more than a quarter of the remainder. At this stage, the Smith boys had together sold just one hundred papers more than the Jones boys had sold. Little Jimmy Jones, the youngest kid in the bunch, now sold all the papers that were left.

The three Jones boys sold more papers than the two Smith boys, but how many more?

2. Notation

Tom Smith = T
Billy Jones = B
Ned Smith = N
Charley Jones = C
Jimmy Jones = J

Total number of papers = t

The Attempt at a Solution

What I gathered from the problem statement.

T = 1/4t + 1
B = 3/16t

After removing Tom Smiths papers, there were t- (1/4)t- 1= (3/4)t-1 papers left. We are told that "Billy Jones disposed of one paper more than a quarter of the remainder": B= (1/4)((3/4)t-1)+ 1= (3/16)t- 1/4+ 1=
(3/16)t+ 3/4. You forgot to take 1/4 of the original "one paper less"

N = 9/64t

"Ned Smith sold one paper more than a quarter of what was left"
"What was left" is now (3/4)t- 1- ((3/16)t+ 3/4)= (9/16)t- 7/4. 1/4 of that is (1/4)((9/16)t- 7/4)= (9/64)t- 7/16. "One paper more" is (9/64)t- 7/16+1= (9/64)t+ 9/16.

C = 27/256t
T + N - 100 = B + C
J = 81/256t - 1

From that I substituted the letters into T + N - 100 = B + C

T + N - 100 = B + C
1/4t + 1 + 9/64t - 100 = 3/16t + 27/256t
1/4t + 9/64t - 99 = 3/16t + 27/256t
25/64t - 99 = 75/256t
25/64t = 75/256t + 99
25/256t = 99
t = 1013 19/25 ??

there can't be a non integer as the no of papers?

im confused, i think i went wrong at some poitn but can't find where, can anyone help? thnx

 

[Trail_Builder]

At this stage, the Smith boys had together sold just one hundred papers more than the Jones boys had sold.

...

T + N - 100 = B + C

wait, i think i might know where i went wrong, when turning the quoted sentence into algabra , is it the case that i need to relate it to the number of papers sold so far?

so should that line look like this?

T(175/256t + 1) + N(175/256t + 1) - 100 = B(175/256t + 1) + C(175/256t + 1)


?

thnx

 

[Trail_Builder]

o rite yeh just saw that reply, thnx buddy