Question 1116185
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            It is a STANDARD ALGEBRA problem,  and it should be solved by Algebra method.



<pre>
The standard and literal translation of the condition to Math is this equation

{{{150/(x-5)}}} - {{{150/x}}} = 1   dollar.


where x is the number of people at the banquet, and each fraction in the left side is the cost (= price) per person.


Simplify and solve it

150x - 150(x-5) = x*(x-5)

750 = x^2 - 5x

x^2 - 5x - 750 = 0

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


The only positive root x= 30 works as the solution to the problem.


<U>Answer</U>.  30 persons.


<U>Check</U>.   {{{150/25}}} - {{{150/30}}} = 6 - 5 = 1.   ! Correct !
</pre>

Solved.


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<U>Again</U>:  &nbsp;&nbsp;It is a standard Algebra problem, &nbsp;and a well trained student must know how to solve it algebraically.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The translation from the condition to Math is the key.  &nbsp;The rest is just technique.


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To see &nbsp;MANY &nbsp;OTHER &nbsp;SIMILAR &nbsp;SOLVED &nbsp;problems, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/misc/Had-they-sold.lesson>Had they sold . . .</A>

in this site.