Hi Paula;

Total box seats...2b

Total reserved seats...2r

Total lawn seats...l

FIRST EQUATION...2b+2r+l=3900

SECOND EQUATION...[2b($10)]+[2r($6)]+[l($4)]=$26,820

The units of dollars on both sides cancels...

................................[2b(10)]+[2r(6)]+[l(4)]=26,820

................................20b+12r+4l=26,820

Divide both sides by 4......5b+3r+l=6,705

THIRD EQUATION...[(b)(10)]+[(r)(6)]+[(l)(4)]=16,190

..............................10b+6r+4l=16,190

Divide both sides by 2.....5b+3r+2l=8,095

Let's subtract the SECOND from the THIRD...

THIRD.........5b+3r+2l=8,095

SECOND...-(5b+3r+l=6,705)

....................**l=1390**

Let's plug l=1390 into all three equations...

FIRST EQUATION...2b+2r+l=3900

............................2b+2r+1390=3900

............................2(b+r)=2510

............................b+r=1255

SECOND EQUATION...5b+3r+l=6705

................................5b+3r+1390=6705

................................5b+3r=5315

THIRD EQUATION...5b+3r+2l=8095

.............................5b+3r+[(2)(1390)]=8095

.............................5b+3r+2780=8095

.............................5b+3r=5315

Let's take the FIRST EQUATION and isolate one variable. I randomly select b...

FIRST EQUATION...b+r=1255

...........................b=1255-r

Let's plug this into the THIRD EQUATION...

THIRD EQUATION...5b+3r=5315

...........................[(5)(1255-r)]+3r=5315

............................6275-5r+3r=5315

............................6275-2r=5315

............................-2r=-960

...........................**r=480**

FIRST EQUATION...2b+2r+l=3900

...........................2b+[(2)(480)]+1390=3900

...........................2b+960+1390=3900

...........................2b+2350=3900

............................2b=1550

.............................**b=775**

SECOND EQUATION...5b+3r+l=6705

................................[(5)(775)]+[(3)(480)]+1390=6705

...............................3875+1440+1390=6705

...............................6705=6705

THIRD EQUATION...5b+3r+2l=8095

............................[(5)(775)]+[(3)(480)]+[(2)(1390)]=8095

............................3875+1440+2780=8095

............................8095=8095

**TOTAL BOX SEATS...2b...(2)(775)=1550**

**TOTAL RESERVE SEATS....2r...(2)(480)=960**

**TOTAL LAWN......l...1390**