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shivusuja

Member

Registered: 2006-09-14

Posts: 56

Quadratic Equation

PLEASE HELP ME OUT IN SOLVING THIS PROBLEM:

SOME STUDENTS PLANNED A PICNIC. THE BUDGET FOR FOOD WAS Rs. 480. BUT EIGHT OF THEM FAILED TO GO AND THUS THE COST FOR EACH MEMBERS INCREASED BY Rs. 10. HOW MANY STUDENTS ATTEND THE PICNIC.

THANK YOU

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Quadratic Equation

Originally, x people would go to the picnic and they would pay 480/x each. But then 8 people don't go, so the remaining people have to pay 10 more each. Therefore, 480/x + 10 = 480/(x-8).
And now that we have the equation, it's just a case of manipulating it until we can solve it.

480/x + 10 = 480/(x-8)

Multiply by x(x-8) to get rid of all denominators: 480(x-8) + 10x(x-8) = 480x
Multiply out of brackets: 480x - 3840 + 10x² - 80x = 480x
Simplify: x² - 8x - 384 = 0
Factorise: (x-24)(x+16) = 0
Solve: x = 24 or -16

So the solution is either 24 or -16. But you can't have a negative amount of people, so we ignore the -16. Therefore, 24 people would have gone to the picnic, which means that 16 people actually did.

Check: With 16 people, they would pay 480/16 = 30 each.
With 24 people, they would pay 480/24 = 20 each.

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Why did the vector cross the road?
It wanted to be normal.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Quadratic Equation

Correct, rechecked it!
You get x, which I called n, equal to 24 or negative 16.
Then you take the 24 and subtract eight people that couldn't make it, which leaves 16 for answer.

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