Question

Hurry quick! If you know how to solve this please let me know step by step because I don't understand the material. Questions are in the attachments.

Answer 1

The system of equation is X+Y=29 and 70X+80Y=2130. John sold 19 General admission tickets and 10 VIP tickets.

Explanation:

System of Equations:

(I)

Let

Number of General Tickets sold = X

Number of VIP Ticket sold = Y

John sold total 29 tickets, including General and VIP tickets.

So, System of equation for total number of tickets is

X+Y=29 (Number of VIP Ticket sold + Number of General Tickets sold = 29)

(II)

His total sales was $2130

Price per General ticket = 70

Price per VIP ticket = 80

Sales from General tickets = 70X (Price per General ticket*Number of General Tickets sold)

Sales from VIP tickets = 80Y (Price per VIP ticket*Number of VIP Tickets sold)

So, Second equation will be

Total Sales = Sales from General tickets + Sales from VIP tickets

$2130 = 70X + 80Y

System of Equations:

X + Y = 29 (Equation 1)

70X+80Y=2130 (Equation 2)

by multiplying Equation 1 with 70 to make the equation solvable.

70X+70Y=29*70

70X+70Y=2030 (Equation 3)

Substracting Equation 3 from Equation 2

(70X+80Y) - (70X+70Y) = 2130 - 2030

70X + 80Y - 70X - 70Y = 100

70X - 70X + 80Y - 70Y = 100

10Y = 100

Y = 100/10

Y = 10

By putting value of Y in Equation 1

X + 10 = 29

X = 29 - 10

X = 19

Check

By putting value of X and Y in Equation 2

70*19 + 80*10 = 2130

1330 + 800 = 2130

2130 = 2130

Hence equation is balanced and the values of X and Y is calculated accurately.

Answer 2

x+y=29

70x+80y=2130

x=19 and y=10

Explanation:

the amount of tickets he sold is 29 which includes VIP and general admission tickets so the number of tickets sold for each would be x+y=29.

the price for general admission is 70$ and VIP is 80$. the profit from the tickets is 2130$ so that would be the number of general tickets (x) times the price (70) and the number of VIP tickets (y) times the price (80) so that would be 80y. therefore you're equation would be 70x+80y=2130. that is your system of equations.

To figure out the number of tickets for each: Solve x+y=29 for x:

x+y=29

x+y+−y=29+−y(Add -y to both sides)

x=−y+29

Substitute−y+29 for xi n70x+80y=2130:

70x+80y=2130

70(−y+29)+80y=2130

10y+2030=2130 (Simplify both sides of the equation)

10y+2030+−2030=2130+−2030 (Add -2030 to both sides)

10y=100

10y/10=100/10 (Divide both sides by 10)

y=10

Substitute 10 for y in x=−y+29:

x=−y+29

x=−10+29

x=19 (Simplify both sides of the equation)

Answer: x=19 and y=10