Question

i'm having trouble translating these problems and solving them... "20,000 tickets were sold to the Green Day concert. Stage level seats cost $105 and higher level seats cost $75. If the total money collected from selling tickets was $1,740,000, how many tickets of each type were sold?"
"write an equation showing 20,000 tickets were sold."
that would be 105x + 75y = 20000 right?
then "write an equation showing $1,740,000 in ticket sales"
and that's where i start to get confused.
then "solve the system of equations to find how many of each type of ticket was sold."
thanks!

Answer 1

Is this multiple choice?

Answer 2

no, i have to write the answer myself

Answer 3

Ugh I wish I was this good at math. I think you would have to do the same to 1,740,000

Answer 4

let 'x' be the number of tickets for $105
'y' be the number of tickets for $75
since there are 20,000 in total then
x + y = 20,000 -----equation 1
total money collected is $1,740,000 then you'll have the equation:
105x + 75y = 1,740,000 ------equation 2
from equation 1
x + y =20,000
x = 20,000 - y ----equation 1'
substitute equation 1' to equation 2
105x + 75y = 1,740,000
105(20,000 - y) + 75y = 1,740,000
2,100,000 - 105y + 75y = 1,740,000
-30y = -360,000
y = 12,000
substitute y=12,000 to equation 1'
x = 20,000 - y
x = 20,000 - 12,000
x = 8,000