Respuesta :
adult: $5, qty x
children: $2, qty y
total: $610, qty 200
Cost: 5x + 2y = 610
Quantity: x + y = 200
Using elimination method to solve the system of equations:
1(5x + 2y = 610) → 5x + 2y = 610
-2( x + y = 200) → -2x - 2y = -400
Add both equations: 3x + 0 = 210
Divide both sides by 3: x = 70
Substitute "x = 70" into either the Cost or Quantity equation:
Quantity: x + y = 200 → 70 + y = 200 → y = 130
Adult tickets sold = 70
Children tickets sold = 130
children: $2, qty y
total: $610, qty 200
Cost: 5x + 2y = 610
Quantity: x + y = 200
Using elimination method to solve the system of equations:
1(5x + 2y = 610) → 5x + 2y = 610
-2( x + y = 200) → -2x - 2y = -400
Add both equations: 3x + 0 = 210
Divide both sides by 3: x = 70
Substitute "x = 70" into either the Cost or Quantity equation:
Quantity: x + y = 200 → 70 + y = 200 → y = 130
Adult tickets sold = 70
Children tickets sold = 130
Thomas sold 70 adult and 130 child tickets.
Total revenue through an Item
The total revenue through an item is the product of its cost per unit and the number of units sold.
[tex]\bold{Total\ revenue = (Cost/unit)\times {Number\ of\ units\ sold}}[/tex]
Given to us,
Ticket cost for adults = $5.00,
Ticket cost for children = $2.00
Total number of ticket sold = 200
Total revenue generated = $610
Assumption
Let's assume that the number of adults tickets sold is x, and the number of children tickets sold is y.
Total number of tickets sold
Total number of tickets sold
= Ticket cost for adults + Ticket cost for children
Substituting the values,
200 = [tex]x+y[/tex]
[tex]x= 200 - y[/tex]
Total revenue generated
Revenue generated through adult ticket
= Ticket cost for adults x number of adults tickets sold
= [tex]\$5 \times x[/tex] = [tex]5x[/tex]
Revenue generated through children ticket
= Ticket cost for children x number of children tickets sold
= [tex]\$2 \times y[/tex] = [tex]2y[/tex]
Total revenue generated
= Revenue through adult ticket +Revenue through children ticket
Substituting the values,
[tex]610 = 5x + 2y[/tex]
Substituting the value of x,
[tex]610 = 5(200-y) + 2y\\610 = 1000-5y + 2y\\610-1000 = -3y\\-390 = -3y\\y = \dfrac{390}{3}\\y = 130[/tex]
Substituting the value of y,
[tex]x = 200- y \\x = 200 -130\\x=70\\[/tex]
Hence, Thomas sold 70 adult and 130 child tickets.
Learn more about cost and revenue:
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