There were 200 students ticket, 450 children ticket and 150 adults ticket sold in that day
Step-by-step explanation:
The given is:
We need to find how many tickets of each type were sold
Assume that there were x tickets for students, y tickets for children and z tickets for adults
∵ A total of 800 tickets were sold
∵ There were x tickets of students
∵ There were y tickets of children
∵ There were z tickets of adults
∴ x + y + z = 800 ⇒ (1)
∵ The cost of a student ticket = $1.5
∵ The cost of a child ticket = $1
∵ The cost of an adult ticket = $2
∵ The total revenue of the tickets were sold is $1050
∴ 1.5(x) + 1(y) + 2(z) = 1050
∴ 1.5 x + y + 2 z = 1050 ⇒ (2)
∵ Three times as many children as adults attended the fair
∴ y = 3 z ⇒ (3)
Substitute equation (3) in equations (1) and (2)
∵ x + 3 z + z = 800
- Add like terms
∴ x + 4 z = 800 ⇒ (4)
∵ 1.5 x + 3 z + 2 z = 1050
- Add like terms
∴ 1.5 x + 5 z = 1050 ⇒ (5)
Let us solve equations (4) and (5)
Multiply equation (4) by -1.5 to eliminate x
∵ -1.5 x - 6 z = -1200 ⇒ (6)
- Add equations (5) and (6)
∴ - z = - 150
- Divide both sides by -1
∴ z = 150
Substitute value of z in equation (3) to find y
∵ y = 3(150)
∴ y = 450
Substitute value of z in equation (4) to find x
∵ x + 4(150) = 800
∴ x + 600 = 800
- Subtract 600 from both sides
∴ x = 200
There were 200 students ticket, 450 children ticket and 150 adults ticket sold in that day
Learn more:
You can learn more about the system of equation in brainly.com/question/9045597
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