Question

Question #45cc2

Answer 1

Read below.

Explanation:

Let's name the advance tickets `a` and the same-day tickets `s`.

`"For one performance, 70 tickets were sold."` This can be rewritten as an equation:
`a+s=70`

`"The total amount paid for them was $2600"` can be rewritten as `35a+40s=2600`

We find `a` in terms of `s` using our first equation.
=>`a+s=70`
=>`a=70-s`

We now substitute this in the place of `a` in the second equation.

`35a+40s=2600=>35(70-s)+40s=2600` We now try to solve the equation.
`=>35(70-s)+40s=2600`
`=>2450-35s+40s=2600`
`=>2450+5s=2600`
`=>5s=150`
`=>s=30`

We use the fact that `a=70-s` to solve for `a`
=>`a=70-s`
=>`a=70-30`
=>`a=40`

We now know that 30 of the same-day tickets and 40 of the advanced tickets were sold.