36 spectators and some performers donated a total of $4500 for a fund-raising project. Each spectator donated $100 more than each performer. If there were 27 more spectators than performers, how much more money did the spectators donate than the performers?
|
Spectators |
Performers |
Total |
Difference |
Number |
36 |
9 |
|
|
Value |
1 u + 100 |
1 u |
|
|
Total value |
36 u + 3600 |
9 u |
45 u + 3600 |
27 u + 3600 |
Amount that the spectators donated
= 36 x (1 u + 100)
= 36 u + 3600
Amount that the performers donated
= 9 x 1 u
= 9 u
Total amount donated
= 36 u + 3600 + 9 u
= 45 u + 3600
45 u + 3600 = 4500
45 u = 4500 - 3600
45 u = 900
1 u = 900 ÷ 45 = 20
Amount of more money donated by the spectators than the performers
= (36 u + 3600) - 9 u
= 27 u + 3600
= (27 x 20) + 3600
= $4140
Answer(s): $4140