some students planned a picnic.The budget for food was 500.but 5 of them failed to go and thus the cost of food for each member increased by Rs.5.How many students attended the picnic ?
Answers
Let the cost of each student be y.
X*y=500
(X-5)(y+5)=500
(x-5)(500/x+5)=500
(X-5)(500+5x/x)=500
500x+5x²/x-2500+25x/x=500
525x+5x²-2500=500x
X²+5x-500=0
(x-20),(x+25)=0
X=20or-25
Answer:
Step-by-step explanation:
I have explained the answer below-----------
Budget for food = ₹ 500 & 5 students failed to attend the picnic.
Let the number of students who planned a picnic be 'x'.
Budget of each student = 500/x
Students who attended the picnic = (x - 5)
New Budget of each student = 500/(x - 5)
A.T.Q
Given : cost of food for each member increased by 20.
(500/x - 5) - (500/x) = 5
[(500 x - 500 (x - 5)] / (x)(x - 5) = 5
500(x - x + 5) / x² - 5x = 5
500(5) / x² - 5x = 5
2500 / x² - 5x = 5
5(x² - 5x) = 2500
x² - 5x = 2500/5
x² - 5x = 500
x² - 5x - 500 = 0
x² - 25x + 20x - 500 = 0
[By middle term splitting method]
x(x - 25) + 20(x - 25) = 0
(x - 25)(x + 20) = 0
(x - 25) = 0 or (x + 20) = 0
x = 25 or x = - 20
Since, number of students can't be negative, so x ≠ - 20.
Therefore, x = 25
Students who attended the picnic = (x - 5) = 25 - 5 = 20
Hence, Students who attended the picnic = 20.
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