SOLUTION: The $75 dollar cost for a party was to be shared equally by all those attending. Since 5 more people attended than was expected, the price per person dropped by 50 cents. How many

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Question 67920This question is from textbook Algebra:Structure and Method
: The $75 dollar cost for a party was to be shared equally by all those attending. Since 5 more people attended than was expected, the price per person dropped by 50 cents. How many people attended the party? This question is from textbook Algebra:Structure and Method

Found 2 solutions by chitra, stanbon:
Answer by chitra(359) About Me  (Show Source):
You can put this solution on YOUR website!
The total cost of the party is = $ 75

Let x be the number of people that have attended the party.

Let the price divided by all the people who have attended the party is = y

Hence, the equation will be:

%2875%2Fx%29+=+y --------------->(1)

Now it is given that 5 more people attended the party. So it is x + 5

And the amount to be shared is reduced by 50 cents.

So it is, y - 0.50

Hence, the equation will be:

%2875%2F%28x%2B5%29%29+=+y+-+0.50 ----------------->(2)

Substituting EQN (1) in EQN (2), we get:


%2875%2F%28x%2B+5%29%29+=+%2875%2Fx%29+-+0.50

+0.50+=+%2875%2Fx%29-+%2875%2F%28x%2B+5%29%29


+0.50+=+%2875%28x+%2B+5%29+-+75x%29%2F%28x%28x%2B5%29%29

0.50+=+%2875x+%2B+375+-+75x%29%2F%28x%28x+%2B+5%29%29

0.50+=+375%2Fx%28x+%2B+5%29

0.50x%28x+%2B+5%29+=+375

%281%2F2%29x%28x+%2B+5%29+=+375

x(x + 5) = 375 * 2

x%5E2 + 5x = 750

x%5E2 + 5x - 750 = 0

This is a quadratic equation, hence by the Method Of Factorization we solve for the value of x.

We observe that the factors of 750 are 25 * 30

So, the equation becomes:

x%5E2 + 30x - 25x - 750 = 0

x(x + 30) - 25(x + 30) = 0

(x - 25)(x + 30) = 0

This implies x = 25 or x = -30

Since 30 is neagtive we cannot take the value. Hence, we take the value 25.

Thus, the total number of people that attended tha party is = 25.

Therefore, y = 25

So when the number of people of increased by 5 then the total number of people who attended the party is y = 30

Hence, the cost per people whould be $ 3 when the number of peopl is 25.

So when there are 30 people, the share of money to be given to the party is $2.50

I hope the steps are clear.

If you have any more queries you can get back to me on this ID. tutyfruty9@yahoo.com

Happy Calculating!!!!












Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The $75 dollar cost for a party was to be shared equally by all those attending. Since 5 more people attended than was expected, the price per person dropped by 50 cents. How many people attended the party?
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Let "x" be the original number attending
Price per person would have been 75/x
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When 5 more attended the number attending was "x+5"
Price per person is then 75/(x+5)
===============
EQUATION:
Old price - New price = 50 cents
75/x - 75/(x+5) = 50
3/x - 3/(x+5) = 2
Multiply thru by x(x+5) to get:
3(x+5) - 3x = 2x(x+5)
3x+15 - 3x = 2x^2+10x
2x^2+10x-15=0
x=[-10+-sqrt(100-4*2*-15)]/4
x=[-10+-sqrt(220)]/4
NOTE: This does not turn to be a whole number.
Please check your problem data.
Cheers,
Stan H.