Question

Example 4: A total of Rs. 3,300 is raised
by collecting equal amounts from a
certain number of people. If there were
22 people more, each person would
have to contribute Rs.200 less to raise
the same amount, how many people
actually contributed?​

Answer 1

answer 11

explanation

let a be the equal amount raised by n people

therefore n*a=3300 --->eq1

given (a-200) (n+22) =3300

=> an-200n+22a-4400=3300

by eq1 3300=an

-200n+22a-4400=0

22a=200n+4400--->eq2

by eq1 a=3300/n

sub in eq2

22(3300/n)=200(n+22)

n2+22n-363=0

n=11 and n=-33

therefore n=11

Answer 2

Answer:

Number of people actually contributed is 11.

Step-by-step explanation:

Given the total amount to be raised $= Rs. 3,300$

Let the amount contributed by each person = $a$

and the number of people contributed $= n$

Therefore $n\times a=3300$                                         ...(1)

Given, if there were 22 people more, each person would have to contribute Rs.200 less to raise the same amount

Therefore $(n+22)(a-200) =3300$

$\implies n\times a+22\times a-n\times 200-22\times 200 =3300$

Using equation (1),

$\implies 3300+22a- 200n-4400 =3300$

$\implies 22 a-200n-4400=0$                                           ...(2)

Equation (1) can also be written as $a=\frac{3300}{n}$

Using this in equation (2),

$\implies 22 \times \frac{3300}{n}-200n-4400=0$

$\implies 22 \times3300-200n^{2} -4400n=0$

Dividing the equation with 200,

$\implies 363-n^{2} -22n=0$

$\implies n^{2} +22n-363=0$

$\implies n^{2} +33n-11n-363=0$

$\implies n(n +33)-11(n+33)=0$

$\implies (n +33)(n-11)=0$

Therefore $n=11$ or $n=-33$

The number of people cannot be a negative number, therefore $n=11$

Therefore, number of people actually contributed is 11.