Question

Some money distributed equally.among children. If 8 children less every one get Rs 10 more. and if there are 16 children more, everyone get Rs 10 less.find total amount .​

Answer 1

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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."

$\frac{a}{(s - 8)} - \frac{a}{s} = 10$

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."

$\frac{a}{s} - \frac{a}{s + 16} = 10$

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.

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▶Hope this Helps uh◀

Answer 2

Answer:

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