Question 164624
Ok, the first thing we need to do is set up our formulas.
Let's use:
r = regular admission tickets = $10
m = members admission tickets = $7
s = student admission tickets = $5
So we know that 750 tickets were sold so:
{{{r+m+s=750}}}

and

We know the price of the tickets and the total dollar amount sold was $5400 so:
Price of each ticket times the number of that ticket sold equals $5400 or:
{{{$10r+$7m+$5s=$5400}}}
We also know that 20 more student tickets than regular tickets were sold so:
{{{s=r+20}}}

Now for the fun part :/)
Use the elimination method to solve:
10r+7m+5s=5400
  r+ m+ s=750
We want to eliminate m because it is the only variable that is not in the s=r+20 equation.
so:
Multiply everything in the bottom equation by 7.
 10r+  7m+  5s=5400
(7)r+(7)m+(7)s=(7)750
OR
10r+7m+5s=5400
 7r+7m+7s=5250
Now we can subtract and get
{{{10r-7r+7m-7m+5s-7s=5400-5250}}}
combine like terms:
{{{3r-2s=150}}}
Now it is time to use the equation: {{{s=r+20}}}
Substitute r+20 for s so:
{{{3r-2(r+20)=150}}}
Distribute
{{{3r-2r-40=150}}}
combine like terms
{{{r-40=150}}}
add 40 to both sides and get {{{r=190}}}
now substitute 190 for r in the equation and solve for s:  {{{s=(190)+20}}}
and you get {{{s=210}}}
go back to the first equation and plug in 190 for r and 210 for s:
{{{r+m+s=750}}}
{{{(190)+m+(210)=750}}}
Solve for m:
combine like terms:
{{{m+400=750}}}
subtract 400 from both sides:
{{{m=350}}}

Elimination and substitution are fun.  It gets better as you get used to them.