Question 1116185
The senior class at a high school had a banquet that cost $150. If there had been one 5 persons less, the cost would have been $1.00 more. how many persons were at the banquet?  
<pre>This is a SIMPLE math problem, and should be just that!!
Let the number of people at the banquet be N
Then cost to each would be: {{{150/N}}}
If there were 5 less people, then the count would be N - 5
We then get the following per person cost-equation: {{{matrix(1,3, 150/N, "=", 150/(N - 5) + 1)}}}
150(N - 5) = 150N + N(N - 5) ------- Multiplying by LCD, N(N - 5)
{{{matrix(1,3, 150N - 750, "=", 150N + N^2 - 5N)}}}
{{{matrix(1,3, N^2 - 5N + 150N - 150N + 750, "=", 0)}}}
{{{matrix(1,3, N^2 - 5N + 750, "=", 0)}}}
(N - 30)(N + 25) = 0
N, or number of people at the banquet = {{{highlight_green(30)}}}             OR                N = - 25 (ignore)