50 spectators and some performers donated a total of $5800 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 |
50 |
30 |
|
|
Value |
1 u + 100 |
1 u |
|
|
Total value |
50 u + 5000 |
30 u |
80 u + 5000 |
20 u + 5000 |
Amount that the spectators donated
= 50 x (1 u + 100)
= 50 u + 5000
Amount that the performers donated
= 30 x 1 u
= 30 u
Total amount donated
= 50 u + 5000 + 30 u
= 80 u + 5000
80 u + 5000 = 5800
80 u = 5800 - 5000
80 u = 800
1 u = 800 ÷ 80 = 10
Amount of more money donated by the spectators than the performers
= (50 u + 5000) - 30 u
= 20 u + 5000
= (20 x 10) + 5000
= $5200
Answer(s): $5200