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?

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Solution

## 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.

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