Question

The tickets for a dance recital cost $5.00 for adults and $2.00 for children. If the total number of tickets sold was 295 and the total amount collected was $1.220, how many adult tickets were sold?

Answer 1

See a solution process below:

Explanation:

First, let's call the number of adult tickets sold: `a`

And, let's call the number of children's tickets sold: `c`

From the information in the problem we can write two equations:

Equation 1: We know 295 tickets we sold so we can write:

`c + a = 295`

Equation 2: We know the cost of adult and children tickets and we know how much total money was collected from ticket sales so we can write:

`$2.50c + $5.00a = $1,220`

Step 1) Solve the first equation for `c`:

`c + a = 295`

`c + a - color(red)(a) = 295 - color(red)(a)`

`c + 0 = 295 - a`

`c = 295 - a`

Step 2) We can now substitute `(295 - a)` for `c` in the second equation and solve for `a`:

`$2.50c + $5.00a = $1,220` becomes:

`$2.50(295 - a) + $5.00a = $1,220`

`($2.50 xx 295) - ($2.50 xx a) + $5.00a = $1,220`

`$737.50 - $2.50a + $5.00a = $1,220`

`$737.50 + (-$2.50 + $5.00)a = $1,220`

`$737.50 + $2.50a = $1,220`

`-color(red)($737.50) + $737.50 + $2.50a = -color(red)($737.50) + $1,220`

`0 + $2.50a = $482.50`

`$2.50a = $482.50`

`($2.50a)/color(red)($2.50) = ($482.50)/color(red)($2.50)`

`(color(red)(cancel(color(black)($2.50)))a)/cancel(color(red)($2.50)) = (color(red)(cancel(color(black)($)))482.50)/color(red)(color(black)(cancel(color(red)($)))2.50)`

`a = 482.50/2.50`

`a = 193`

The Answer Is: 193 Adult Tickets Were Sold