A local band sells out for their concert. They sell all 1,175 tickets for a total purse of $28,112.50.

Question

A local band sells out for their concert. They sell
all 1,175 tickets for a total purse of $28,112.50. The
tickets were priced at $20 for student tickets, $22.50
for children, and $29 for adult tickets. If the band
sold twice as many adult as children tickets, how
many of each type was sold?

Answer 1

S + C + A = 1175

 

20S + 22.50C + 29A = 28112.50

 

A = 2C

 

------------------------------------------

 

Substitutes the third equation into the first and second

so that variable A is eliminated.

 

S + C + 2C = 1175

 

20S + 22.50C + 29(2C) = 28112.50

 

--------------------------------------------------

 

combines like terms and cleans it up:

 

S + 3C = 1175

 

20S + 80.5C = 28112.50

 

--------------------------------------------------

 

Solves the first equation for S and multiplies

the second by 10 so as to clear away the decimals:

 

S = 1175 - 3C <--- label this equation ALPHA; we need it later... you'll see

 

200S +805C = 281125

 

---------------------------------------

 

Substitutes the top equation:

 

200( 1175 - 3C) + 805C = 281125

 

235000 - 600C + 805C = 281125

 

235000 - 600C + 805C - 281125  = 0

 

205C - 46125 = 0

 

C = 46125/205 = 225

 

225 children's tickets

 

plugging this into equation ALPHA above  (told ya' we were gonna need it   ;-)

S = 1175 - 3*225 = 500

 

500 student tix

 

A = 1175 - 500 - 225 = 450

 

450 adult 

 

CHECK

 

$20*500 + 22.50*225 + 29*450 = $28112.5

 

Yes!!! It works, the answer is correct, tried, tested,and proven.