34 spectators and some performers donated a total of $5300 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 |
34 |
4 |
|
|
Value |
1 u + 100 |
1 u |
|
|
Total value |
34 u + 3400 |
4 u |
38 u + 3400 |
30 u + 3400 |
Amount that the spectators donated
= 34 x (1 u + 100)
= 34 u + 3400
Amount that the performers donated
= 4 x 1 u
= 4 u
Total amount donated
= 34 u + 3400 + 4 u
= 38 u + 3400
38 u + 3400 = 5300
38 u = 5300 - 3400
38 u = 1900
1 u = 1900 ÷ 38 = 50
Total amount donated
= 34 u + 3400 + 4 u
= 38 u + 3400
38 u + 3400 = 5300
38 u = 5300 - 3400
38 u = 1900
1 u = 1900 ÷ 38 = 50
Amount of less money donated by the performers than the spectators
= (34 u + 3400) - 4 u
= 30 u + 3400
= (30 x 50) + 3400
= $4900
Answer(s): $4900