35 spectators and some performers donated a total of $5300 for a fund-raising project. 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 |
35 |
5 |
|
|
Value |
1 u + 100 |
1 u |
|
|
Total value |
35 u + 3500 |
5 u |
40 u + 3500 |
30 u + 3500 |
Amount that the spectators donated
= 35 x (1 u + 100)
= 35 u + 3500
Amount that the performers donated
= 5 x 1 u
= 5 u
Total amount donated
= 35 u + 3500 + 5 u
= 40 u + 3500
40 u + 3500 = 5300
40 u = 5300 - 3500
40 u = 1800
1 u = 1800 ÷ 40 = 45
Amount of more money donated by the spectators than the performers
= (35 u + 3500) - 5 u
= 30 u + 3500
= (30 x 45) + 3500
= $4850
Answer(s): $4850