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an amount is distributed equally among a certain no. of students.
if there are 8 students less, everyone will get Rs.10 more.
if there are 16 students more, each will get Rs.10 less.
what is the no. of students and the amount each gets?
what is the total amount distributed?
Let a = total amt
Let s = number of student
"If there are 8 students less, everyone will get Rs.10 more."
Multiply by s(s-8)
as - a(s-8) = 10s(s-8)
as - as + 8a = 10s^2 - 80s
8a = 10s^2 - 80s
"if there are 16 students more, each will get Rs.10 less."
Multiply by s(s+16)
a(s+16) - as = 10s(s+16)
as + 16a - as = 10s^2 + 160s
16a = 10s^2 + 160s
divide by 2
8a = 5s^2 + 80s
8a = 8a, therefore combine the two equations
10s^2 - 80s = 5s^2 + 80s
10s^2 - 5s^2 - 80s - 80s = 0
5s^2 - 160s = 0
Factor out s
5s - 160 = 0
5s = 160
s = 160/5
s = 32 students
Find the amt using 8a = 5s^2 + 80s, replace s with 32
8a = 5(32^2) + 80(32)
8a = 5120 + 2560
8a = 7680
a = 7680/8
a = $960 total distributed
Find the total for each student:
960/32 = $30 each student
Check this using the statement:
"If there were 8 less, each get $10 more
960/24 = $40, for each
You can check it in the other statement