A theater sold a total of 100 tickets for a performance, consisting of standard tickets (s… — GMAT

A theater sold a total of $100$ tickets for a performance, consisting of standard tickets ( $s$ ) at $\$25$ each and VIP tickets ( $v$ ) at $\$50$ each. The total revenue from ticket sales was $\$3,500$ . Match each ticket category to the correct number of tickets sold.

Standard Tickets ( $s$ )60
VIP Tickets ( $v$ )40

Answer

Standard Tickets matches to 60; VIP Tickets matches to 40.

The correct matches are Standard Tickets to 60 and VIP Tickets to 40 because solving the system

s + v = 100

and

25s + 50v = 3500

gives

s = 60

and

v = 40

Step-by-Step Solution

Set up the simultaneous linear equations from the text.

s + v = 100

and

25s + 50v = 3500

The total count equation represents total tickets, and the price equation represents total revenue.

Divide the revenue equation by 25 to simplify terms.

s + 2v = 140

Simplifying the coefficients reduces calculation complexity.

Subtract the first equation (

s + v = 100

) from the simplified second equation (

s + 2v = 140

v = 40

Subtracting eliminates the variable

s

directly.

Substitute

v = 40

back into

s + v = 100

s = 60

Yields the value for the remaining variable

s

Key Concept

Solving simultaneous linear equations in two variables.

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