49 spectators and some performers donated a total of $5500 for a charity drive. Each spectator donated $100 more than each performer. If there were 23 more spectators than performers, how much more money did the spectators donate than the performers?
|
Spectators |
Performers |
Total |
Difference |
Number |
49 |
26 |
|
|
Value |
1 u + 100 |
1 u |
|
|
Total value |
49 u + 4900 |
26 u |
75 u + 4900 |
23 u + 4900 |
Amount that the spectators donated
= 49 x (1 u + 100)
= 49 u + 4900
Amount that the performers donated
= 26 x 1 u
= 26 u
Total amount donated
= 49 u + 4900 + 26 u
= 75 u + 4900
75 u + 4900 = 5500
75 u = 5500 - 4900
75 u = 600
1 u = 600 ÷ 75 = 8
Amount of more money donated by the spectators than the performers
= (49 u + 4900) - 26 u
= 23 u + 4900
= (23 x 8) + 4900
= $5084
Answer(s): $5084