Which system of equations represents this situation?

Question

A hip-hop dance crew sold 50 tickets to its showcase. Each general ticket cost $8, and each VIP ticket cost $15. The crew collected a total of $505 from these ticket sales. Let g represent the number of general tickets sold and v represent the number of VIP tickets sold.

Accepted Answer

A. g + v = 50 and 8g + 15v = 505. The number of tickets sold gives g + v = 50, and the money collected gives 8g + 15v = 505, since each general ticket contributes $8 and each VIP ticket contributes $15. Choice B interchanges the ticket count (50) with the dollar total ($505). Choice C attaches each price to the wrong variable, charging $15 for general tickets and $8 for VIP tickets. Choice D misreads 'sold 50 tickets' as a difference between the two ticket types rather than a total.

Answer

B. g + v = 505 and 8g + 15v = 50 — You swapped the two totals: 50 is the number of tickets and $505 is the money collected, so 50 belongs with g + v and 505 with the priced equation.

Answer

C. g + v = 50 and 15g + 8v = 505 — You matched the prices to the wrong variables — general tickets cost $8 (so 8g) and VIP tickets cost $15 (so 15v).

Answer

D. g − v = 50 and 8g + 15v = 505 — "Sold 50 tickets" means the two types add to 50, so the equation is g + v = 50, not a difference.

Algebra practice question

Answer: A. g + v = 50 and 8g + 15v = 505

Why the other answers are wrong

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