Question

Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $30 and same-day tickets cost $25. For
there were 60 tickets sold in all, and the total amount paid for them was $ 1625. How many tickets of each type were sold?
performance,
X
Number of advance tickets sold:
Number of same-day tickets sold: I
6
?

Answer 1

The number of advance tickets sold is 25 and same day tickets sold is 30.

Data Given;

• Advance Ticket = $30
• Same-day Ticket = $25
• Total Ticket = $60
• Total Cost of Ticket = $1625

System of Equations

Let the number of advance ticket be represented by x

Let the number of same-day ticket be represented by y

$x + y = 60\\ 30x + 25y = 1625$

From the system of equations above, we can easily pick any to start our calculation.

Using equation (i),

x + y = 60

x = 60 - y ...equation(iii)

Put equation (iii) into equation (ii)

$30x + 25y = 1625\\ x = 60 - y\\ 30(60 - y) + 25y = 1625\\ 1800 - 30y + 25y = 1625\\ 1800 -5y = 1625\\ 5y = 1800 - 1625\\ 5y = 175\\ 5y/5 = 175/5\\ y = 35$

Put the value of y into equation (i)

$x+y = 60\\ x + 35 = 60\\ x = 60 - 35\\ x = 25$

From the calculation above, the number of advance tickets sold is 25 and same-day tickets is 30.

Learn more on system of equations here;

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