system of linear equations

Question

Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost
$20
and same-day tickets cost
$25
. For one performance, there were
65
tickets sold in all, and the total amount paid for them was
$1500
. How many tickets of each type were sold?

Answer 1

Let x represent $20 tickets

let y represent $25 tickets

 

x+y=65...equation 2

20(x)+25(y)=1500...equation 1

 

x+y=65

20x+25y=1500

 

to find y multiple equation 2 by 20 to eliminate x

 

20 (x+y=65)

 20x +25y=1500

 20x+20y=1300

========== subtract equations

       5y=200

 

y=200/5= 40

 

x+40=65

x=65-40

 

x=25

 

to check

20(25)+25(40)=

500+1000=$1500 check