36 spectators and some performers donated a total of $4900 for a fund-raising project. Each spectator donated $100 more than each performer. If there were 20 more spectators than performers, how much less money did the performers donate than the spectators?
|
Spectators |
Performers |
Total |
Difference |
Number |
36 |
16 |
|
|
Value |
1 u + 100 |
1 u |
|
|
Total value |
36 u + 3600 |
16 u |
52 u + 3600 |
20 u + 3600 |
Amount that the spectators donated
= 36 x (1 u + 100)
= 36 u + 3600
Amount that the performers donated
= 16 x 1 u
= 16 u
Total amount donated
= 36 u + 3600 + 16 u
= 52 u + 3600
52 u + 3600 = 4900
52 u = 4900 - 3600
52 u = 1300
1 u = 1300 ÷ 52 = 25
Total amount donated
= 36 u + 3600 + 16 u
= 52 u + 3600
52 u + 3600 = 4900
52 u = 4900 - 3600
52 u = 1300
1 u = 1300 ÷ 52 = 25
Amount of less money donated by the performers than the spectators
= (36 u + 3600) - 16 u
= 20 u + 3600
= (20 x 25) + 3600
= $4100
Answer(s): $4100