some students planned a picnic .the budget for food was rupees 480 but eight of these failed to go and thus cost of food for each member increase by rupees 10 how many students attended the picnic
Answers
SOLUTION :
Given : Budget for food = ₹ 480
Let the number of students planned a picnic be x .
Share of each student = 480/x
8 students failed to go to picnic , the remaining students = (x - 8)
New share for each student = 480/(x - 8)
480/(x - 8) = 480/x + 10
480/(x - 8) - 480/x = 10
480[1/(x - 8) - 1/x ] = 10
1/(x - 8) - 1/x = 10/480
[x - (x - 8)] / x(x -8) = 1/48
[By taking LCM]
[x - x + 8)] / x² - 8x = 1/48
8/ x² - 8x = 1/48
x² - 8x = 8 × 48
x² - 8x = 384
x² - 8x - 384 = 0
x² + 16x - 24x - 384 = 0
[By middle term splitting]
x(x + 16) - 24(x + 16) = 0
(x - 24)(x + 16) = 0
(x - 24) = 0 or (x + 16) = 0
x = 24 or x = - 16
Since, number of students can't be negative, so x ≠ - 16
Therefore , x = 24
The number of students planned a picnic be 24.
Number of students attended the picnic = (x - 8) = 24 - 8 = 16
Hence, the number of students attended the picnic be 16 .
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Answer:
Step-by-step explanation:
Let the number of students planned a picnic be x .
Share of each student = 480/x
8 students failed to go to picnic , the remaining students = (x - 8)
New share for each student = 480/(x - 8)
480/(x - 8) = 480/x + 10
480/(x - 8) - 480/x = 10
480[1/(x - 8) - 1/x ] = 10
1/(x - 8) - 1/x = 10/480
[x - (x - 8)] / x(x -8) = 1/48
[By taking LCM]
[x - x + 8)] / x² - 8x = 1/48
8/ x² - 8x = 1/48
x² - 8x = 8 × 48
x² - 8x = 384
x² - 8x - 384 = 0
x² + 16x - 24x - 384 = 0
[By middle term splitting]
x(x + 16) - 24(x + 16) = 0
(x - 24)(x + 16) = 0
(x - 24) = 0 or (x + 16) = 0
x = 24 or x = - 16
Since, number of students can't be negative, so x ≠ - 16
Therefore , x = 24
The number of students planned a picnic be 24.
Number of students attended the picnic = (x - 8) = 24 - 8 = 16
Hence, the number of students attended the picnic be 16 .
HOPE THIS ANSWER WILL HELP YOU...