50 spectators and some performers donated a total of $5700 for a donation drive. Each spectator donated $100 more than each performer. If there were 30 more spectators than performers, how much more money did the spectators donate than the performers?
| |
Spectators |
Performers |
Total |
Difference |
| Number |
50 |
20 |
|
|
| Value |
1 u + 100 |
1 u |
|
|
| Total value |
50 u + 5000 |
20 u |
70 u + 5000 |
30 u + 5000 |
Amount that the spectators donated
= 50 x (1 u + 100)
= 50 u + 5000
Amount that the performers donated
= 20 x 1 u
= 20 u
Total amount donated
= 50 u + 5000 + 20 u
= 70 u + 5000
70 u + 5000 = 5700
70 u = 5700 - 5000
70 u = 700
1 u = 700 ÷ 70 = 10
Amount of more money donated by the spectators than the performers
= (50 u + 5000) - 20 u
= 30 u + 5000
= (30 x 10) + 5000
= $5300
Answer(s): $5300
