32 spectators and some performers donated a total of $4600 for a fund-raising project. Each spectator donated $100 more than each performer. If there were 29 more spectators than performers, how much more money did the spectators donate than the performers?
|
Spectators |
Performers |
Total |
Difference |
Number |
32 |
3 |
|
|
Value |
1 u + 100 |
1 u |
|
|
Total value |
32 u + 3200 |
3 u |
35 u + 3200 |
29 u + 3200 |
Amount that the spectators donated
= 32 x (1 u + 100)
= 32 u + 3200
Amount that the performers donated
= 3 x 1 u
= 3 u
Total amount donated
= 32 u + 3200 + 3 u
= 35 u + 3200
35 u + 3200 = 4600
35 u = 4600 - 3200
35 u = 1400
1 u = 1400 ÷ 35 = 40
Amount of more money donated by the spectators than the performers
= (32 u + 3200) - 3 u
= 29 u + 3200
= (29 x 40) + 3200
= $4360
Answer(s): $4360