SOLUTION: the $75 cost for a party was to be shared equally by all those attending. since five more people attended than was expected, the price per person dropped by $.50. how many people a

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Question 253118: the $75 cost for a party was to be shared equally by all those attending. since five more people attended than was expected, the price per person dropped by $.50. how many people attended the party?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
the $75 cost for a party was to be shared equally by all those attending.
since five more people attended than was expected, the price per person dropped by $.50.
how many people attended the party?
:
Let x = no. that actually attended
then
(x-5) = no. that were anticipated to attend
:
Anticipated cost/person - actual cost/person = $.50
75%2F%28%28x-5%29%29 - 75%2Fx = 1%2F2; (we're dealing in dollars here)
Multiply equation by 2x(x-5), results:
2x(75) - 2(x-5)(75) = x(x-5)
:
150x - 75(2x-10) = x^2 - 5x
:
150x - 150x + 750 = x^2 - 5x
:
Arrange as a quadratic equation
0 = x^2 - 5x - 750
factors to:
(x - 30)(x + 25) = 0
Positive solution
x = 30 people actually attended
;
:
Check this by finding the cost for each person
75/25 = $3.00; anticipated
75/30 = $2.50; actual