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?
Correct answer: D. 75B + 40L = 19,250B + L = 350
- A. (75B) + (40L) = 1,950B + L = 350
- B. 40B + 75L = 19,250B + L = 350
- C. 75B + 40L = 350B + L = 19,250
- D. 75B + 40L = 19,250B + L = 350
Explanation
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.
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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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