Question

(100 POINTS PLEASE HELP ME MY GRADE RELY ON IT)

Last weekend, the movie theatre sold a total of 8,500 movie tickets. Proceeds totaled around 64,600.
There are three ways to buy a movie ticket. Matinee tickets costs $5, student tickets is $6 all day, and regular tickets are $8.50.
Twice as many student tickets were sold than
Matinee. Please write the system of equations.
(SHOULD BE 3 EQUATIONS)

Answer 1

Answer:

x= number of matinee tickets sold = 900

y= number of student tickets sold = 1800

z= number of regular tickets sold = 5800

steps below.

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Answer 2

Answer:

System of equations:

$\begin{cases}m + s + r = 8500\\5m + 6s + 8.5r = 64600\\s = 2m\end{cases}$

(where m is the number of Matinee tickets sold, s is the number of Student tickets sold and r is the number of Regular tickets sold).

Step-by-step explanation:

Given information:

• Total tickets sold = 8,500
• Total proceeds = $64,600
• Cost of Matinee ticket = $5
• Cost of Student ticket = $6
• Cost of Regular ticket = $8.50
• Twice as many Student tickets were sold than Matinee tickets.

Define the variables:

• Let m = number of Matinee tickets sold.
• Let s = number of Student tickets sold.
• Let r = number of Regular tickets sold.

Equation for the total tickets sold:

• m + s + r = 8500

Equation for the total proceeds:

• 5m + 6s + 8.5r = 64600

Equation for twice as many Student tickets were sold than Matinee tickets:

• s = 2m

Therefore, the system of equations is:

$\begin{cases}m + s + r = 8500\\5m + 6s + 8.5r = 64600\\s = 2m\end{cases}$

Solving the system of equations

To solve the found system of equations, substitute the third equation into the first equation and isolate r:

$\implies m+2m+r=8500$

$\implies 3m+r=8500$

$\implies r=8500-3m$

Substitute the found expression for r and the third equation into the second equation and solve for m:

$\implies 5m+6(2m)+8.5(8500-3m)=64600$

$\implies 5m+12m+72250-25.5m=64600$

$\implies 72250-8.5m=64600$

$\implies 8.5m=7650$

$\implies m=900$

Therefore, the total number of Matinee tickets sold was 900.

Substitute the found value of m into the third equation and solve for s:

$\implies s=2(900)$

$\implies s=1800$

Therefore, the total number of Student tickets sold was 1800.

Substitute the found value of m into the found equation for r and solve for r:

$\implies r=8500-3(900)$

$\implies r=8500-2700$

$\implies r=5800$

Therefore, the total number of Regular tickets sold was 5800.