31 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 22 more spectators than performers, how much less money did the performers donate than the spectators?
|
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 = 4900
40 u = 4900 - 3100
40 u = 1800
1 u = 1800 ÷ 40 = 45
Total amount donated
= 31 u + 3100 + 9 u
= 40 u + 3100
40 u + 3100 = 4900
40 u = 4900 - 3100
40 u = 1800
1 u = 1800 ÷ 40 = 45
Amount of less money donated by the performers than the spectators
= (31 u + 3100) - 9 u
= 22 u + 3100
= (22 x 45) + 3100
= $4090
Answer(s): $4090