Question

1500 distributed among neighbors and each would have 5 less there had been 10 more neighbors

Answer 1

Answer:

number of neighbors = 50

Step-by-step explanation:

let no of neighbors = x

total amount = 1500

share for each neighbor = 1500/x

no of neighbors with 10 more neighbors = x+10

share for each neighbor now = 1500/(x+10)

given, 1500/(x+10) = 1500/x - 5

=> 1500/x - 1500/(x+10) = 5

=> 1500{1/x - 1/(x+10)} = 5

=> 1500{(x+10)-x}/{x(x+10)} = 5

=> 1500(x+10-x)/5 = x(x+10)

=> 3000 = x^2 + 10x

=> x^2 + 10x - 3000 = 0

=> x = {-10 +- √(100 + 12000)}/2

=> x = {-10 +- √12100}/2

=> x = {-10 +- 110}/2

=> x = {-10 + 110}/2 or x = {-10 - 110}/2

=> x = 50 or x = -60 (no of negative neighbors is impossible)

So total number of neighbors = 50