37 spectators and some performers donated a total of $5000 for a fund-raising project. Each spectator donated $100 more than each performer. If there were 24 more spectators than performers, how much less money did the performers donate than the spectators?
|
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 = 5000
50 u = 5000 - 3700
50 u = 1300
1 u = 1300 ÷ 50 = 26
Total amount donated
= 37 u + 3700 + 13 u
= 50 u + 3700
50 u + 3700 = 5000
50 u = 5000 - 3700
50 u = 1300
1 u = 1300 ÷ 50 = 26
Amount of less money donated by the performers than the spectators
= (37 u + 3700) - 13 u
= 24 u + 3700
= (24 x 26) + 3700
= $4324
Answer(s): $4324