39 spectators and some performers donated a total of $5100 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 |
39 |
9 |
|
|
Value |
1 u + 100 |
1 u |
|
|
Total value |
39 u + 3900 |
9 u |
48 u + 3900 |
30 u + 3900 |
Amount that the spectators donated
= 39 x (1 u + 100)
= 39 u + 3900
Amount that the performers donated
= 9 x 1 u
= 9 u
Total amount donated
= 39 u + 3900 + 9 u
= 48 u + 3900
48 u + 3900 = 5100
48 u = 5100 - 3900
48 u = 1200
1 u = 1200 ÷ 48 = 25
Amount of more money donated by the spectators than the performers
= (39 u + 3900) - 9 u
= 30 u + 3900
= (30 x 25) + 3900
= $4650
Answer(s): $4650