Posted by Andrew on Monday, February 21, 2011 at 9:28pm.
The $75 cost for a party was to be shared equally by all of those attending. Since five more people attended than was expected, the price per person dropped by 50 cents. How many people attended the party?

Algebra  Reiny, Monday, February 21, 2011 at 9:41pm
original cost per person = 75/x
new cost per person = 75/(x+5)
75/x  75(x+5) = 1/2
multiply each term by x(x+5)
75(x+5)  75x = (1/2)x(x+5)
times 2
150x + 750  150x = x^2 + 5x
x^2 + 5x  750 = 0
(x25)(x+30) = 0
x = 25 or x = 30 , but clearly x > 0
x=25
originally 25 had planned to attend, but 30 actually did.
check:
cost with 25 = 75/25 = $3.00
cost with 30 = 75/30 = $2.50
it cost 50 cents less.
Answer is correct.