Question

How can i solve this? I've looked at countless videos and nothing helps.

Answer 1

Let
`x` be the number of lower-level tickets sold, and
`y` the number of upper-level tickets sold.

Now, if the theater sells 350 tickets total, that means the number of lower-level and upper-level tickets that got sold should add up to 350, so one equation in the system is


`x+y=350`

You also know that the theater earns $10250 in sales, so if each lower-level ticket costs $35, and each upper-level ticket costs $25[/tex], this means
`35x` represents the amount of money made from selling lower-level ticekts, and
`25y` represents the amount of money made from selling upper-level tickets. You get the second equation in the system,


`35x+25y=10250`

So the system is


`\begin{cases}x+y=350\\35x+25y=10250\end{cases}`

Any one of the methods listed in the second part works in solving this system (though I'm not sure what "variable" refers to), but I think substituting involves the least work.

Solve the first equation for either variable; I'll choose
`x`.


`x+y=350\implies x=350-y`

Now substitute this into the second equation for
`x`, then solve for
`y`.


`35(350-y)+25y=10250\implies 10y=2000\implies y=200`

So 200 upper-level seats were sold. Meanwhile, since
`x+y=350`, this means


`x+200=350\implies x=150`

so that 150 lower-level tickets were sold.