43 spectators and some performers donated a total of $5900 for a fund-raising project. Each spectator donated $100 more than each performer. If there were 22 more spectators than performers, how much more money did the spectators donate than the performers?
|
Spectators |
Performers |
Total |
Difference |
Number |
43 |
21 |
|
|
Value |
1 u + 100 |
1 u |
|
|
Total value |
43 u + 4300 |
21 u |
64 u + 4300 |
22 u + 4300 |
Amount that the spectators donated
= 43 x (1 u + 100)
= 43 u + 4300
Amount that the performers donated
= 21 x 1 u
= 21 u
Total amount donated
= 43 u + 4300 + 21 u
= 64 u + 4300
64 u + 4300 = 5900
64 u = 5900 - 4300
64 u = 1600
1 u = 1600 ÷ 64 = 25
Amount of more money donated by the spectators than the performers
= (43 u + 4300) - 21 u
= 22 u + 4300
= (22 x 25) + 4300
= $4850
Answer(s): $4850