30 spectators and some performers donated a total of $4200 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 |
30 |
10 |
|
|
Value |
1 u + 100 |
1 u |
|
|
Total value |
30 u + 3000 |
10 u |
40 u + 3000 |
20 u + 3000 |
Amount that the spectators donated
= 30 x (1 u + 100)
= 30 u + 3000
Amount that the performers donated
= 10 x 1 u
= 10 u
Total amount donated
= 30 u + 3000 + 10 u
= 40 u + 3000
40 u + 3000 = 4200
40 u = 4200 - 3000
40 u = 1200
1 u = 1200 ÷ 40 = 30
Total amount donated
= 30 u + 3000 + 10 u
= 40 u + 3000
40 u + 3000 = 4200
40 u = 4200 - 3000
40 u = 1200
1 u = 1200 ÷ 40 = 30
Amount of less money donated by the performers than the spectators
= (30 u + 3000) - 10 u
= 20 u + 3000
= (20 x 30) + 3000
= $3600
Answer(s): $3600