Question

Solving a value mixture problem using a system of linear...

Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is $55. For
one performance, 35 advance tickets and 25 same-day tickets were sold. The total amount paid for the tickets was $1675. What was the price of each kind of
ticket?

Answer 1

Advance - $30

Same day - $25

Explanation:

Notice that if 35 advance and 25 same-day were sold, that means 25 "combos" and 10 advance tickets. 25 combos cost 25*$55=$1375

That leaves $1675-$1375=$300 for the advance tickets.

10 advance tickets cost $300, so 1 costs $300/10 = $30.

That means a same-day ticket costs $55-$30=$25.

Just to reverify:

35*$30 + 25*$25 = $1675.