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

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) (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:

--------------->(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:

----------------->(2)

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

x(x + 5) = 375 * 2

+ 5x = 750

+ 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:

+ 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) (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?
------------------
Let "x" be the original number attending
Price per person would have been 75/x
---------------------------------------
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.

RELATED QUESTIONS
the 75 dollar cost for a party was to be equally shared by all those attending. Since 5... (answered by mananth)
The $75 cost for a party was to be shared equally by all those attending. Since 5 more... (answered by richwmiller)
the $75 cost for a party was to be shared equally by all those attending. since five more (answered by ankor@dixie-net.com)
The $75 cost for a party was to be shared equally by all those attending. Since five more (answered by Paul)
The rent of a condo unit was P1,200.00 for one night, to be shared equally by a group of... (answered by ankor@dixie-net.com)
The cost of a bus excursion was $180. This amount was to have been shared equally by all... (answered by mananth,stanbon)
The number of students attending the fall play was 150 more than the number of adults... (answered by ewatrrr)
The cost of hiring a bus for an outing was $240 and this was to be shared equally by X... (answered by josgarithmetic)
The cost p, in dollars, of having a dinner party catered by Elain's Kosher Catering... (answered by checkley77)