John is selling tickets to an event. Attendees can either buy a general admission ticket, x,
or a VIP ticket, y. The general admission tickets are $50 and the VIP tickets are $55. If he
knows he sold a total of 29 tickets and made $1,505, how many of each type did he sell?
Enter a system of equations to represent the situation, then solve the system.
The system of equations is
and
John sold
general admission tickets and
VIP tickets.

Question

contestada

Respuesta :

absor201 absor201 · Answer 1 · 2020-01-25T13:48:35+01:00

John sold 18 general admission tickets and 11 VIP tickets.

Step-by-step explanation:

Given,

Cost of each general admission = $50

Cost of each VIP ticket = $55

Total tickets sold = 29

Total revenue generated = $1505

Let,

x represent the number of general admission tickets sold

y represent the number of VIP tickets.

x+y=29 Eqn 1

50x+55y=1505 Eqn 2

Multiplying Eqn 1 by 50

[tex]50(x+y=29)\\50x+50y=1450\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](50x+55y)-(50x+50y)=1505-1450\\50x+55y-50x-50y=55\\5y=55[/tex]

Dividing both sides by 5

[tex]\frac{5y}{5}=\frac{55}{5}\\y=11[/tex]

Putting y=11 in Eqn 1

[tex]x+11=29\\x=19-11\\x=18[/tex]

John sold 18 general admission tickets and 11 VIP tickets.

Keywords: linear equation, elimination method

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