Question

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?

Answer 1

370

Explanation:

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

`"how_much"="total_price"/"price"`

`"how_much"=740/2`

`"how_much"=370`

Answer 2

`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`