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1.	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?
Answer» 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.

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?

Answer»

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.

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