40 spectators and some performers donated a total of $5500 for a fund-raising project. Each spectator donated $100 more than each performer. If there were 20 more spectators than performers, how much more money did the spectators donate than the performers?
|
Spectators |
Performers |
Total |
Difference |
Number |
40 |
20 |
|
|
Value |
1 u + 100 |
1 u |
|
|
Total value |
40 u + 4000 |
20 u |
60 u + 4000 |
20 u + 4000 |
Amount that the spectators donated
= 40 x (1 u + 100)
= 40 u + 4000
Amount that the performers donated
= 20 x 1 u
= 20 u
Total amount donated
= 40 u + 4000 + 20 u
= 60 u + 4000
60 u + 4000 = 5500
60 u = 5500 - 4000
60 u = 1500
1 u = 1500 ÷ 60 = 25
Amount of more money donated by the spectators than the performers
= (40 u + 4000) - 20 u
= 20 u + 4000
= (20 x 25) + 4000
= $4500
Answer(s): $4500