A theater sold 500 tickets amoumting to Rs. 6000 in one show. The tickets were sold to adults for Rs. 15 and to children for Rs. 5 each. How many adults and children attended the show?
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Answer:
350 and 150
Step-by-step explanation:
Let the no. of adults be ' x ' and children be ' y '
Total tickets sold = 500
=> x + y = 500 ............... eq 1
Ticket cost for adult = 15
.°. Total amount collected from adults = 15x
Ticket cost for children = 5
.°. Total amount collected from children = 5y
Total amount collected = Rs. 6000
=> 15x + 5y = 6000.......... eq 2
Subtract eq 1 from eq 2
=> 15x + 5y = 6000
- ( x + y = 500 )
=> 15x + 5y = 6000
- x - y = - 500
Multiply eq 2 by 5 to equalte
=> 15x + 5y = 6000
- 5x - 5y = -2500
=> 10x = 3500
=> x = 3500/ 10 = 350
Substitute x = 350 in eq 1
x + y = 500
=> 350 + y = 500
=> y = 500 - 350
=> y = 150
No. of adults attended the show = 350
No. of children attended the show = 150
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