31 spectators and some performers donated a total of $5500 for a donation drive. Each spectator donated $100 more than each performer. If there were 22 more spectators than performers, how much more money did the spectators donate than the performers?
| |
Spectators |
Performers |
Total |
Difference |
| Number |
31 |
9 |
|
|
| Value |
1 u + 100 |
1 u |
|
|
| Total value |
31 u + 3100 |
9 u |
40 u + 3100 |
22 u + 3100 |
Amount that the spectators donated
= 31 x (1 u + 100)
= 31 u + 3100
Amount that the performers donated
= 9 x 1 u
= 9 u
Total amount donated
= 31 u + 3100 + 9 u
= 40 u + 3100
40 u + 3100 = 5500
40 u = 5500 - 3100
40 u = 2400
1 u = 2400 ÷ 40 = 60
Amount of more money donated by the spectators than the performers
= (31 u + 3100) - 9 u
= 22 u + 3100
= (22 x 60) + 3100
= $4420
Answer(s): $4420
