Question

Atkins athletic department sold adult tickets for $5 and student tickets for $2. They sold a total of 202 tickets and collected a total of $764. How many adult tickets did they sell?

Answer 1

Given:

The cost of adult tickets = $5.

The cost of student tickets = $2.

The total number of tickets = 202.

The total cost = $764.

Aim:

We need to find the cost of the adult ticket.

Step-by-step explanation:

Let x be the number of adult tickets.

Let y be the number of student tickets

Given that the total number of tickets is 202.

`x+y=202`

Substract x from both sides of the equation.

`y=202-x`

Given that the total cost is $764.

`5x+2y=764`

`\text{ Substitute }y=202-x\text{ in the equation to find the value of x.}`

`5x+2(202-x)=764`

Solve for x.

`5x+404-2x=764`

`5x-2x=764-404`

`3x=360`

Divide both sides by 3.

`(3x)/(3)=(360)/(3)`
`x=120`

Final answer:

The number of adult tickets = 120 tickets.