Using a system of linear equations

Question

Problem Page
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
$60
. For one performance,
30
advance tickets and
25
same-day tickets were sold. The total amount paid for the tickets was
$1700
. What was the price of each kind of ticket?

Answer 1

Suppose the cost of advance ticket is $X, because the combined cost of the advance ticket and the same-day ticket is $60, so the cost of same-day ticket is $(60-X).

 

30 advanced tickets were sold, so the total amount paid for the advanced tickets was $30X;

25 same-day tickets were sold, so the total amount paid for same-day tickets was $25(60-X);

The total amount paid for the tickets was $1700.

 

So we can set up the equation, it would be:

$30X + $25(60-X) = 1700

$30X + $1500 -$25X = 1700 (distributive property)

5X = $200 (combination and subtraction)

X = $40 (divided by 5)

$60-$X = $20 

 

So, the price of advanced ticket is $40, the price of same-day ticket is $20.