34 spectators and some performers donated a total of $5800 for a charity drive. 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 |
34 |
14 |
|
|
Value |
1 u + 100 |
1 u |
|
|
Total value |
34 u + 3400 |
14 u |
48 u + 3400 |
20 u + 3400 |
Amount that the spectators donated
= 34 x (1 u + 100)
= 34 u + 3400
Amount that the performers donated
= 14 x 1 u
= 14 u
Total amount donated
= 34 u + 3400 + 14 u
= 48 u + 3400
48 u + 3400 = 5800
48 u = 5800 - 3400
48 u = 2400
1 u = 2400 ÷ 48 = 50
Total amount donated
= 34 u + 3400 + 14 u
= 48 u + 3400
48 u + 3400 = 5800
48 u = 5800 - 3400
48 u = 2400
1 u = 2400 ÷ 48 = 50
Amount of less money donated by the performers than the spectators
= (34 u + 3400) - 14 u
= 20 u + 3400
= (20 x 50) + 3400
= $4400
Answer(s): $4400