35 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 30 more spectators than performers, how much less money did the performers donate than the spectators?
|
Spectators |
Performers |
Total |
Difference |
Number |
35 |
5 |
|
|
Value |
1 u + 100 |
1 u |
|
|
Total value |
35 u + 3500 |
5 u |
40 u + 3500 |
30 u + 3500 |
Amount that the spectators donated
= 35 x (1 u + 100)
= 35 u + 3500
Amount that the performers donated
= 5 x 1 u
= 5 u
Total amount donated
= 35 u + 3500 + 5 u
= 40 u + 3500
40 u + 3500 = 4900
40 u = 4900 - 3500
40 u = 1400
1 u = 1400 ÷ 40 = 35
Total amount donated
= 35 u + 3500 + 5 u
= 40 u + 3500
40 u + 3500 = 4900
40 u = 4900 - 3500
40 u = 1400
1 u = 1400 ÷ 40 = 35
Amount of less money donated by the performers than the spectators
= (35 u + 3500) - 5 u
= 30 u + 3500
= (30 x 35) + 3500
= $4550
Answer(s): $4550