Two types of tickets were sold for a concert held at an amphitheater. Tickets to sit on a bench during the concert cost $75 each, and tickets to sit on the lawn during the concert cost $40 each. Organizers of the concert announced that 350 tickets had been sold and that $19,250 had been raised through ticket sales alone. Which of the following systems of equations could be used to find the number of tickets for bench seats, B, and the number of tickets for lawn seats, L, that were sold for the concert?

Question

TestUstad · Accepted Answer

75B + 40L = 19,250B + L = 350. Choice D is correct. Since only two types of tickets were sold and a total of 350 tickets were sold, the sum of the numbers of both types of ticket sold must be 350. Therefore, B + L = 350. Since the bench tickets were $75 each, the income from B bench tickets was 75B. Similarly, since the lawn tickets were $40 each, the income from L lawn tickets sold was 40L. The total income from all tickets was $19,250. So the sum of the income from bench tickets and lawn tickets sold must equal 19,250. Therefore, 75B + 40L = 19,250. Only choice D has both correct equations.

TestUstad · Answer

(75B) + (40L) = 1,950B + L = 350

TestUstad · Answer

40B + 75L = 19,250B + L = 350

TestUstad · Answer

75B + 40L = 350B + L = 19,250

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