Tickets to a concert cost $10 in advance and $15 at the door, so if 120 tickets were sold for a total of $1390, how many of the tickets were purchased in advance?

Question

Tickets to a concert cost $10 in advance and $15 at the door. If 120 tickets were sold for a total of $1390, how many of the tickets were purchased in advance? (Please show steps)

Answer 1

Tickets to a concert cost $10 in advance and $15 at the door, so if 120 tickets were sold for a total of $1390, how many of the tickets were purchased in advance?

Let X be the number of tickets sold in advance

Let Y be the number of tickets sold at the door

Then,

X + Y = 120    (total number of tickets sold)

X*$10 + Y*$15 = $1390    (total revenue from sales)

Substituting for X = 120 - Y into the money equation,

(120 - Y)*10 + Y *15 = 1390

1200 - 10Y + 15Y = 1390

5Y = 190

Y = 38

X = 120 - 38

X = 82

Answer: 82 tickets sold in advance, 38 tickets sold at the door.

Answer 2

let a is the price of an advanced ticket and d is the price of a ticket at the door.

It will be; a+d=120 (1)  and 10a+15d=1390 (2)  from the (1) we get  d=120-a putting this value to (2)

we get; 10a+15(120-a)=1390  --->>>  10a+1800-15a=1390 ---->>> -5a=1390-1800  and -5a=-410

multiplyiing both sides by -1 we have 5a=410 and a=410/5=82

so 82 tickets were sold in advance.  (120-82=38 tickets sold at the door so d=38)