37 spectators and some performers donated a total of $4400 for a fund-raising project. Each spectator donated $100 more than each performer. If there were 24 more spectators than performers, how much more money did the spectators donate than the performers?
|
Spectators |
Performers |
Total |
Difference |
Number |
37 |
13 |
|
|
Value |
1 u + 100 |
1 u |
|
|
Total value |
37 u + 3700 |
13 u |
50 u + 3700 |
24 u + 3700 |
Amount that the spectators donated
= 37 x (1 u + 100)
= 37 u + 3700
Amount that the performers donated
= 13 x 1 u
= 13 u
Total amount donated
= 37 u + 3700 + 13 u
= 50 u + 3700
50 u + 3700 = 4400
50 u = 4400 - 3700
50 u = 700
1 u = 700 ÷ 50 = 14
Amount of more money donated by the spectators than the performers
= (37 u + 3700) - 13 u
= 24 u + 3700
= (24 x 14) + 3700
= $4036
Answer(s): $4036