Each participant paid $25 to attend a workshop. On Saturday, the number of female participants was 130 fewer than the number of male participants. On Sunday, the number of male participants decreased by 20% while the number of female participants increase by 20%. There were 574 participants on Sunday. Find the total amount of money paid by all the participants on both day.
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Question
Answer
Hope it helps π
Let the number of male participants attending the workshop on Saturday be M.
Saturday
Number of Ladies: M-130
Number of Guys : M
Sunday
Number of Ladies: (M -130) x 120% = 1.2M – 156
Number of Guys : M x 80% = 0.8M
Thus, on Sunday, the total number of participants = (1.2M-156)+0.8M = 574
2M = 830 (Should be 730 instead)
M = 415
Number of female participants on Saturday = 415 -130 = 285
Total number of participants on Saturday= 415 + 285 = 700
Total amount of money paid = (700 x $25) + (574 x $25)
Hi JC – Math, thank you so much.Β
Hi JC-Math .com, thanks for your prompt reply.
the answer given was $ 29,350. thank.
Though it is possible to edit my earlier post, I will make a modification to my workings and highlight my mistakes in blue. Let’s learn from my mistake!
It is possible to solve this question using the number of ladies or guys on Saturday as a reference. Arosisi’s approach used the number of ladies attending the workshop on Saturday as a reference, that is 100%. My workings will be using the number of guys on Saturday as 100%.Β
The earlier post’s method is based on algebra. If it is not a suitable method, you can consider percentage method + model diagram in arosisi’s postΒ
Percentage Method
Let the number of male participants attending the workshop on Saturday be 100%.
Saturday
Number of Guys : 100%
Number of Ladies: 100%-130
Sunday
Number of Guys : 100% x 80% = 80%
Number of Ladies: (100% -130) x 120% = 120% β 156
Thus, on Sunday, the total number of participants = (120%-156)+80% βΒ 574
200% βΒ 574+156 = 730
100% βΒ 365
Number of female participants on Saturday = 365 -130 = 235
Total number of participants on Saturday= 365 + 235 = 600
Total amount of money paid = (600 + 574) x $25
Hi JC-Math, really appreciated your detail explanation. thanks again.
Sat
F -> 100%
M -> 100% + 130
Total -> 200% + 130
Sun
F -> 100% + 20% = 120%
M -> 100% + 130 – 20% – 26 = 80% + 104
Total -> 200% + 104
200% + 104 = 574
200% = 574 – 104 = 470
Total (Sat) = 470 + 130 = 600
Total (Sat+Sun) = 600 + 574 = 1174
Total sum of money = 1174 x $25 = $29350 (Ans)
Hope it helps π