Question

A class decided to have a party for their class at a total cost of rs.1450. Four students decided to stay out of the party. To meet the expense the remaining students have to increase their shares by rs.8. What is the original share per students?

Answer 1

Let the number of students=x, and share of each=y.

So, the first equation:-

xy=1450……(1)

y=1450/x……(a)

Now, 4 students did not come, so each student had to increase their share by ₹ 8.

So, the second equation:-

(x-4)(y+8)=1450

xy+8x-4y-32=1450

xy+8x-4y=1482……(2)

Now, putting the value of eqn (a) in eqn (2):-

x×1450/x+8x-4×1450/x=1482

1450+8x-5800/x=1482

8x²-5800-32x/x=0

8x²-5800-32x=0

-8(-x²+4x+725)=0

-8(-x²+29x-25x+725)=0

-8(-x×(x-29)-25(x-29))=0

-8(-(x-29)(x+25))=0

8(x-29)(x+25)=0

(x-29)(x+25)=0

So, the two solutions are:- 29 and -25

But here, we will consider the positive solution only.

So, x=29……(b)

Now, putting eqn (b) value in eqn (1):-

29×y=1450

y=1450/29

y=50

So, original share per student=₹ 50

Verification:-

•For first equation:

xy=1450……(1)

29×50=1450

1450=1450

So, LHS = RHS, hence verified.

•For second equation:

(x-4)(y+8)=1450

(29-4)(50+8)=1450

25×58=1450

1450=1450

So, LHS = RHS, hence verified.