At a theme park, each adult ticket cost $35 and each child ticket cost $10. On Tuesday, the number of adult tickets sold was 50 less than the number of child tickets. On Wednesday, the number of adult tickets sold decreased by 5% while the number of child tickets sold increased by 50%. If a total of 1300 tickets were sold on Wednesday, how much money was collected on Tuesday?
|
Adult tickets |
Child tickets |
Total tickets |
Before |
1 u |
1 u + 50 |
2 u + 50 |
Change |
- 0.05 u |
+ 0.5 u + 25 |
|
After |
0.95 u |
1.5 u + 75 |
2.45 u + 75 |
5% x 1 u =
5100 x 1 u = 0.05 u
50% x 1 u =
50100 x 1 u = 0.5 u
50% x 50 =
50100 x 50 = 25
Number of tickets sold on Wednesday
= 0.95 u + 1.5 u + 75
= 2.45 u + 75
2.45 u + 75 = 1300
2.45 u = 1300 - 75
2.45 u = 1225
1 u = 1225 ÷ 2.45 = 500
Amount collected from adult tickets on Tuesday
= 1 u x 35
= 500 x 35
= $17500
Amount collected from child tickets on Tuesday
= 10(1 u + 50)
= 10(500 + 50)
= 10 x 550
= $5500
Total amount collected on Tuesday
= 17500 + 5500
= $23000
Answer(s):$23000