Students can buy tickets to a basketball game for $2.00. The admission for nonstudents is $3.00. If 340 tickets are sold and the total receipts are $740, how many student tickets are sold?

2 Answers
Apr 10, 2017

370

Explanation:

#"price"=2#
#"total_price"=740#
#"how_much"=x#

#"how_much"="total_price"/"price"#

#"how_much"=740/2#

#"how_much"=370#

Apr 11, 2017

#280# student tickets were sold.

Explanation:

There are two different prices for tickets: #$2 or $3#

Students pay #2# and other people pay #3#.

Let the number of students be #x#
Let the number of other people be #y#

The money paid by all the students is #x xx $2 = $2x#
The money paid by all the others is #y xx $3 = $3y#

We can make two equations:
One for the total number of people: #" "x+y = 340#
One for the total amount of money #" " 2x+3y = 740#

Solve them for #x and y#

#color(white)(.......................)x+y = 340" "A#
#color(white)(.....................)2x+3y = 740" "B#
#A xx -2:-2x-2y = -680" "C#

#B+C:" "y=60#

If #y=60, " then "x = 340-60 = 280#

There were #280# students and #60# other people:

Check:

#280# students pay #$2 = $560#
#60" "# others pay #$3 = $180#

Total#color(white)(.....................)=$740#