Question

For a science exhibition, tickets for children cost 2 rupees and for adults, 5 rupees. 100 tickets were sold for one show, and 290 rupees was got. How many children were there for this show?

Answer 1

Cost of ticket for children = Rs.2

Cost of ticket for adults = Rs.5

Total number of tickets sold = 100

Total money collected = Rs.290

Let the number of tickets sold for children be x.

The number of tickets sold for adults = 100 − x

Total cost collected from the tickets sold for children = Rs.2x

Total cost collected from the tickets sold for adults = Rs 5(100 − x) = Rs (500 − 5x)

Algebraic form of the problem is:

2x + 500 − 5x = 290

⇒ 500 − 3x = 290

Adding 3x to both the sides:

500 − 3x + 3x = 290 + 3x

⇒ 500 = 290 + 3x

Subtracting 290 from both the sides:

⇒ 500 − 290 = 290 + 3x − 290

⇒ 210 = 3x

Dividing both the sides by 3:

Therefore, there were 70 children in the show.