Four hundred entrance tickets were sold for a school fair. The cost of the ticket for adults was Rs. 20
Four hundred entrance tickets were sold for a school fair. The cost of the ticket for adults was Rs. 20 and that for students was Rs. 10. The total collection from of the sale of entrance tickets was Rs. 6000. How many adults visited the fair?
1 Answers
Step 1. Formulation of the problem
We know that
The total number of tickets sold = 400
The cost of a ticket for adults = Rs. 20
The cost of the ticket for student = Rs. 10
and the total proceedings were = Rs. 6000
Mathematical formulation : Let the number of adults who visited the fair be x
∴ number of students visited = (400 - x)
Total amount received from adults = Rs. 20x
Total amount received from students = Rs. 10(400 - x)
Total amount collected = Rs. 6000
∴ the model (relation) is 20x + 10(400 - x) = 6000
Step 2. Finding the solutions
20x + 4000 - 10x = 6000
=> 10x + 4000 = 6000
=> 10x = 2000
=> x = 200
Step 3. Interpretation of the solution
We assumed that the number of adults who visited the fair was x
∴ 200 adults visited the fair.
Step 4. Validation of the result
No. of adults who visited the fair = 200
No. of students who visited the fair = (400 - 200) = 200
∴ Total receipts = Rs (20 × 200) + Rs. (10 × 200)
= Rs. 4000 + Rs. 2000
= Rs. 6000
Thus, the total collection from 200 adults and 200 students is Rs. 6000.