find the answer
some students planned a picnic budget for food was Rs 500 but five of them failed to go and thus the cost of food for each member increased by Rs 5 . how many students attend the picnic
Answers
Let x = original number of planned attendees
Let y = cost per person
xy = 500 {equation 1}
(x-5)(y+5) = 500 {equation 2}
From equation 2:
xy + 5x - 5y - 25 = 500
We know xy = 500 so
500 + 5x - 5y - 25 = 500
5x - 5y - 25 = 0
5(x-y-5) = 0
x - y - 5 = 0
From equation 1: y = 500/x
x - 500/x - 5 = 0
Multiply through by x
x2 - 500 - 5x = 0
x2 - 5x - 500 = 0
This can be factored. The factors of -500 that add to -5 are -25(20)
(x-25)(x+20) = 0
x = 25 or x = -20
Discarding the negative, x = 25
This was the original planned numbers for attendance.
The actual number that attended was x-5
20 students attended.
hope it helps......
# Aniket ✌️
Step-by-step explanation:
Let x = original number of planned attendees
Let y = cost per person
xy = 500 {equation 1}
(x-5)(y+5) = 500 {equation 2}
From equation 2:
xy + 5x - 5y - 25 = 500
We know xy = 500 so
500 + 5x - 5y - 25 = 500
5x - 5y - 25 = 0
5(x-y-5) = 0
x - y - 5 = 0
From equation 1: y = 500/x
x - 500/x - 5 = 0
Multiply through by x
x2 - 500 - 5x = 0
x2 - 5x - 500 = 0
This can be factored. The factors of -500 that add to -5 are -25(20)
(x-25)(x+20) = 0
x = 25 or x = -20
Discarding the negative, x = 25
This was the original planned numbers for attendance.
The actual number that attended was x-5
20 students attended