[Guest]

this week's lottery winners won by a syndicate of 10 people. between them they won $2,775,000. they all contributed different amounts into the syndicate and their winnings were calculated aganist their contributions. if the amounts were all different but the cash differences between each step remained uniform, what amount did the second-highest get given that the lowest three amounts was equal to the sum of the top two amounts?

$330,000 ($15,000 increments)

[bonanova]

Your answer is correct

[Guest]

Try not to show the answer with the question. Wait to show the answer.

[Guest]

this week's lottery winners won by a syndicate of 10 people. between them they won $2,775,000. they all contributed different amounts into the syndicate and their winnings were calculated aganist their contributions. if the amounts were all different but the cash differences between each step remained uniform, what amount did the second-highest get given that the lowest three amounts was equal to the sum of the top two amounts?

I used the formulas we learned in school for arithmetic progression A1, A2, ...An, with common difference = d

If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence is given by: An = A1+(n-1)d and the Sum = n(A1 + An)/2

In addition for this case we are told

A1+A2+A3 = A9+A10

we know that sum = 2,775,000 and want to find A9 and d

use the first formula to substitute A1+(n-1)d for all An in the second and third formulas then you'll have two formulas and two unknowns, solve for A1 and d and the rest falls out.

A1 = 210,000

d=15,000

Therefore

Second highest (A9) got $330,000

Uniform cash difference was $15,000

Edited February 14, 2009 by Loretta

[Guest]

correct!!!!!!!!!!!!

[Guest]

Don't show your answer wait til someone gets it

[Guest]

someone just told me that

[Guest]

ertx

Edited February 15, 2009 by psychrn

[Guest]

ertx