A concert raises $3540 from ticket sales to 250 people. Children tickets were sold for $12 and adult tickets for $18. Find the number of children and adults who attended the concert.
Answers
Given :
Total amount raised by the concert = $3540
Total number of people who attended the concert = 250
Cost of each child ticket = $12
Cost of each adult ticket = $18
To find :
The number of children and adults who attended the concert.
Solution :
• Let the number of children who attended the concert be x.
• Since the cost of each child ticket is $12, the cost of tickets for x children is x × $12 = $12x.
• Number of adults who attended the concert = Total number of people who attended the concert - Number of children who attended the concert
=> Number of adults who attended the concert = 250 - x
• Since the cost of each ticket for an adult is $18, the cost of tickets for (250 - x) adults is (250 - x) × $18.
• According to the question,
$12x + (250 - x) × $18 = $3540
Taking out 6$ as the common factor, we get;
=> $6 [ 2x + (250 - x) × 3 ] = $3540
=> $6 [ 2x + (250 × 3) - (x × 3) ] = $3540
=> $6 [ 2x + 750 - 3x ] = $3540
=> 750 - 3x + 2x = $3540 / $6
=> 750 - x = 590
=> 750 - 590 = x
=> x = 160
∴ Number of children = 160
Number of adults = 250 - 160 = 90
Answer : Number of children who attended the concert = 160
Number of adults who attended the concert = 90
Given :
Total amount = $3540
Total number of people = 250
Child ticket = $12
Adult ticket = $18
To find :
The number of children and adults who attended the concert.
Method Used:
Method presented here in this solution is based on a Mathematical Heuristic called "Assumption Method".
Solution
First, assumed all the tickets are child tickets:
Total tickets cost = 250 x 12
Total tickets cost = $3000
Find the difference between the assumption and the question:
Assumption gives us $3000 but the question said that the amount was $3540
Difference = 3540 - 3000
Difference = $540
Find the difference in the price of the two tickets:
Adult ticket = $18
Child ticket = $12
Difference =18 - 12
Difference = $6
Find the number of adult tickets:
The difference of $540 must have came from the sales of adult tickets.
Number of adult tickets = 540 ÷ 6
Number of adult tickets = 90
Find the number of child tickets:
Total Tickets = 250
Adult Tickets = 90
Child Tickets = 250 - 90
Child Tickets = 160
Answer: There are 160 children and 90 adult attended the concert.