38 spectators and some performers donated a total of $5200 for a charity drive. Each spectator donated $100 more than each performer. If there were 20 more spectators than performers, how much more money did the spectators donate than the performers?
|
Spectators |
Performers |
Total |
Difference |
Number |
38 |
18 |
|
|
Value |
1 u + 100 |
1 u |
|
|
Total value |
38 u + 3800 |
18 u |
56 u + 3800 |
20 u + 3800 |
Amount that the spectators donated
= 38 x (1 u + 100)
= 38 u + 3800
Amount that the performers donated
= 18 x 1 u
= 18 u
Total amount donated
= 38 u + 3800 + 18 u
= 56 u + 3800
56 u + 3800 = 5200
56 u = 5200 - 3800
56 u = 1400
1 u = 1400 ÷ 56 = 25
Amount of more money donated by the spectators than the performers
= (38 u + 3800) - 18 u
= 20 u + 3800
= (20 x 25) + 3800
= $4300
Answer(s): $4300