50 spectators and some performers donated a total of $5300 for a donation drive. Each spectator donated $100 more than each performer. If there were 25 more spectators than performers, how much more money did the spectators donate than the performers?
|
Spectators |
Performers |
Total |
Difference |
Number |
50 |
25 |
|
|
Value |
1 u + 100 |
1 u |
|
|
Total value |
50 u + 5000 |
25 u |
75 u + 5000 |
25 u + 5000 |
Amount that the spectators donated
= 50 x (1 u + 100)
= 50 u + 5000
Amount that the performers donated
= 25 x 1 u
= 25 u
Total amount donated
= 50 u + 5000 + 25 u
= 75 u + 5000
75 u + 5000 = 5300
75 u = 5300 - 5000
75 u = 300
1 u = 300 ÷ 75 = 4
Amount of more money donated by the spectators than the performers
= (50 u + 5000) - 25 u
= 25 u + 5000
= (25 x 4) + 5000
= $5100
Answer(s): $5100