At a concert hall, each adult ticket cost $24 and each child ticket cost $14. On Tuesday, the number of adult tickets sold was 70 less than the number of child tickets. On Wednesday, the number of adult tickets sold decreased by 35% while the number of child tickets sold increased by 40%. If a total of 1123 tickets were sold on Wednesday, how much money was collected on Tuesday?
|
Adult tickets |
Child tickets |
Total tickets |
Before |
1 u |
1 u + 70 |
2 u + 70 |
Change |
- 0.35 u |
+ 0.4 u + 28 |
|
After |
0.65 u |
1.4 u + 98 |
2.05 u + 98 |
35% x 1 u =
35100 x 1 u = 0.35 u
40% x 1 u =
40100 x 1 u = 0.4 u
40% x 70 =
40100 x 70 = 28
Number of tickets sold on Wednesday
= 0.65 u + 1.4 u + 98
= 2.05 u + 98
2.05 u + 98 = 1123
2.05 u = 1123 - 98
2.05 u = 1025
1 u = 1025 ÷ 2.05 = 500
Amount collected from adult tickets on Tuesday
= 1 u x 24
= 500 x 24
= $12000
Amount collected from child tickets on Tuesday
= 14(1 u + 70)
= 14(500 + 70)
= 14 x 570
= $7980
Total amount collected on Tuesday
= 12000 + 7980
= $19980
Answer(s):$19980