Question 356334
For the band concert,students tickets cost $2 and adult tickets cost $5.a total of 200 tickets were sold . If the total sales were more than $500 , what was the minimum number of adult tickets sold ? 

{{{system(a + s = 200,
2s + 5a > 500)}}}

We'll start out pretending that the total sales were exactly $500 (as though
fractions of people could by fractions of tickets:

So we solve this system:

{{{system(a + s = 200,
2s + 5a = 500)}}}

and get {{{500/3}}} or {{{166&2/3}}} student tickets and {{{100/3}}} or {{{33&1/3}}}

But they must be whole numbers not fractions. So we try 

s = 166 and a = 33  
s = 166 and a = 34
s = 167 and a = 33
s = 167 and a = 34

to see which gives the minimum amount over $500

s = 166 and a = 33, 2s + 5a = $492, not enough  
s = 166 and a = 34, 2s + 5a = $502, may be the minimum
s = 167 and a = 33, 2s + 5a = $499, not enough
s = 167 and a = 34, 2s + 5a = $504, so $502 is the minimum

To exceed $500, minimum is when 166 student tickets, and 34 adult tickets are sold.

Answer: 34 is the minimum number of adult tickets that could be sold
and the intake be more than $500. 

Edwin</pre>