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 . For one performance, advance tickets and same-day tickets were sold. The total amount paid for the tickets was . What was the price of each kind of ticket

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 $ 40. For one performance, 25 advance tickets and 30 same-day tickets were sold. The total amount paid for the tickets was $1075 . What was the price of each kind of ticket?

Let

advance tickets=x

Same-day tickets=y

Combined cost of advance and same-day tickets=$40

It means,

x+y=40 Equ (1)

25 advance tickets and 30 same-day tickets=$1075

It means,

25x+30y=1075 Equ(2)

From (1)

x+y=40

x=40-y

Substitute x=40-y into (2)

25x+30y=1075

25(40-y)+30y=1075

1000-25y+30y=1075

5y=1075-1000

5y=75

Divide both sides by 5

5y/5=75/5

y=15

Recall,

x+y=40

x+15=40

x=40-15

=25

x=25

Advance tickets=$25

Same-day tickets=$15

Check

25x+30y=1075

25(25)+30(15)=1075

625+450=1075

1075=1075