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 as :
The money raises from ticket sales = $3540
The price of each children ticket = $12
The price of each adult ticket = $18
Total number of tickets sold = 250
To Find :
The number of children and adults who attended the concert .
Solution :
Let The number of children who attended the concert = $c
Let The number of adults who attended the concert = $a
According to question
∵ Total number of tickets sold = 250
So, Total number of people = 250
i.e number of adults + number of children = 250
Or, a + c = 250 ....................1
Total money raises from ticket sales = price of each adult ticket × number of adults + price of each children ticket × number of children
Or, a × $18 + c × $12 = $3540
Or, 18 a + 12 c = 3540
Or, 3 a + 2 c = 590 .............2
Solving eq 1 and 2
( 3 a + 2 c ) - 3 × ( a + c ) = 590 - 3 × 250.
Or, ( 3 a - 3 a ) + ( 2 c - 3 c ) = 590 - 750
Or, ( 0 ) + ( - c ) = - 160
∴ c = 160
So, The number of children who attended the concert = c = 160
Put the value of a into eq 1
∵ a + c = 250
i.e a + 160 = 250
Or, a = 250 - 160
∴ a = 90
So, The number of adults who attended the concert = a = 90
Hence, The number of children who attended the concert is 160
And The number of adults who attended the concert is 90 Answer
Such questions can be solved by a mathematic heuristic called the Assumption Method. This method does not require algebra knowledge to solve the problem.
Assumption Method starts by making a assumption that all belongs to one variables and nothing to the other. This allows us to solve by finding the difference between the assumption and the question.
Given:
Total value of the tickets sold = $3540
Total number of people = 250.
Child ticket = $12
Adult ticket = $18
Assumed all are child tickets:
Child tickets = $12
Total tickets = 250
Total amount = 12 x 250 = $3000
Observation => If all the 250 tickets are child tickets, then the price would be $3000
Find the difference between the assumption and the question:
Difference = $3540 - $3000
Difference = $540
Observation => The difference of $540 must be made up by the adult tickets.
Find the difference in price of the two tickets:
Child ticket = $12
Adult ticket = $18
Difference = 18 - 12
Difference = $6
Find the number of adult tickets:
Number of adult tickets = 540 ÷ 6
Number of adult tickets = 90
Observation => There are 90 adult tickets.
Find the number of tickets:
Adult tickets = 90
Child tickets = 250 - 90
Child tickets = 160
Answer: There are 160 child tickets and 90 adult tickets.
Check:
Chid tickets = 160 x $12
Chid tickets = $1920
Adult tickets = 90 x $18
Adult tickets = $1620
Total = 1920 + 1620
Total = $ 3540 (Checked)