42 spectators and some performers donated a total of $5300 for a donation drive. Each spectator donated $100 more than each performer. If there were 29 more spectators than performers, how much more money did the spectators donate than the performers?
|
Spectators |
Performers |
Total |
Difference |
Number |
42 |
13 |
|
|
Value |
1 u + 100 |
1 u |
|
|
Total value |
42 u + 4200 |
13 u |
55 u + 4200 |
29 u + 4200 |
Amount that the spectators donated
= 42 x (1 u + 100)
= 42 u + 4200
Amount that the performers donated
= 13 x 1 u
= 13 u
Total amount donated
= 42 u + 4200 + 13 u
= 55 u + 4200
55 u + 4200 = 5300
55 u = 5300 - 4200
55 u = 1100
1 u = 1100 ÷ 55 = 20
Amount of more money donated by the spectators than the performers
= (42 u + 4200) - 13 u
= 29 u + 4200
= (29 x 20) + 4200
= $4780
Answer(s): $4780