At a museum, each adult ticket cost $32 and each child ticket cost $8. On Monday, the number of adult tickets sold was 146 less than the number of child tickets. On Tuesday, the number of adult tickets sold decreased by 45% while the number of child tickets sold increased by 50%. If a total of 2064 tickets were sold on Tuesday, how much money was collected on Monday?
|
Adult tickets |
Child tickets |
Total tickets |
Before |
1 u |
1 u + 146 |
2 u + 146 |
Change |
- 0.45 u |
+ 0.5 u + 73 |
|
After |
0.55 u |
1.5 u + 219 |
2.05 u + 219 |
45% x 1 u =
45100 x 1 u = 0.45 u
50% x 1 u =
50100 x 1 u = 0.5 u
50% x 146 =
50100 x 146 = 73
Number of tickets sold on Tuesday
= 0.55 u + 1.5 u + 219
= 2.05 u + 219
2.05 u + 219 = 2064
2.05 u = 2064 - 219
2.05 u = 1845
1 u = 1845 ÷ 2.05 = 900
Amount collected from adult tickets on Monday
= 1 u x 32
= 900 x 32
= $28800
Amount collected from child tickets on Monday
= 8(1 u + 146)
= 8(900 + 146)
= 8 x 1046
= $8368
Total amount collected on Monday
= 28800 + 8368
= $37168
Answer(s):$37168