40 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 30 more spectators than performers, how much more money did the spectators donate than the performers?
|
Spectators |
Performers |
Total |
Difference |
Number |
40 |
10 |
|
|
Value |
1 u + 100 |
1 u |
|
|
Total value |
40 u + 4000 |
10 u |
50 u + 4000 |
30 u + 4000 |
Amount that the spectators donated
= 40 x (1 u + 100)
= 40 u + 4000
Amount that the performers donated
= 10 x 1 u
= 10 u
Total amount donated
= 40 u + 4000 + 10 u
= 50 u + 4000
50 u + 4000 = 4600
50 u = 4600 - 4000
50 u = 600
1 u = 600 ÷ 50 = 12
Amount of more money donated by the spectators than the performers
= (40 u + 4000) - 10 u
= 30 u + 4000
= (30 x 12) + 4000
= $4360
Answer(s): $4360