Question

54. Parking receipts. Parking fees at a zoo are $5.00 for local residents and $7.50 for all others. At the end of each day, the total number of vehicles parked that day and the gross receipts for the day are recorded, but the number of vehicles in each category is not. The following table contains the relevant information for a recent 4-day period: Day 1 2 3 4 Vehicles parked 1,200 1,550 1,740 L 1.400 Gross receipts | $7,125 $9,825 $11,100 $8,650 (A) How many vehicles in each category used the zoo's parking facilities each day? (B) If 1,200 vehicles are parked in one day, is it possible to take in gross receipts of $5,000? Of $10,000? Explain. (C) Describe all possible gross receipts on a day when 1.200 vehicles are parked.

Answer 1

Aus. A) het & for Da re be the wood velicles packed at Zool. y be the no of vehicles parked at local residents. According to queath for Day 2 Day 1000 sety 1200 ? solving we get 5x+75y =7825 J xotro, y..450 Vehicles packed at zoo 750 Vehicles parked at local residents = 450 for Day 2, aty = 1550 sehing we get, 5x+8y = 903 420,830 ..l vehicles packed at 200 = 720 I vehicles parted at local residents = 830 for Day 3, x+y = 1740 we get, 54+.xy = /1100 x2780 4.960 Vehicles poulted at 200 = 40 Neticles packed at lonal residents = 960 for ay 49 dety=1400 l solving we get, 5x+#.5y = 8650 Vehicles packed at 200= 740 velieles palked at local residents = 660 Ares: B) bross receipt of $5000 x+y = 1200 ? we get x=1600 & y = -400 We got 571 +.5y = 5000 hele velviles pauted at local residents is negative ie, - 400 which is not possible hell I we get, and grows receipt of $10000 x+y = 1200 50+5.5y = 10000 - 400 y 1600 We got here, velicles parked at zoo is negative ine - 400 which is not possible here, Therefore gross receipt of $5000 & $10000 daoth are not possible