Question

At homecoming, 125 tickets where sold. Tickets purchased for homecoming cost $20.5 without an activity card, and $15.75 with an activity card. $2365 was made in total. What amount of students had an activity card? What amount did not?

Answer 1

Nearly 83 students did not had activity card.

Nearly 42 students had an activity card.

Explanation:

Total number of tickets sold at homecoming = 125

Cost of each ticket without activity card = $20.5

Cost of each ticket with activity card = $15.75

Total amount earned = $2365

Let, the number of tickets sold without activity car d = k

So, the number of tickets sold without card = (Total sold - k)

= 125 - k

Now, according to the question:

$20.5(k) + $15.75(125 - k) = $2365

or, 20.5 k + 1968.5 - 15.75 k = 2365

⇒ 4.75 k = 2365 - 1968.5 = 396.5

⇒
`k = (396.5)/(4.75 )  = 83.47`

Hence, nearly 83 students did not had activity card.

So,the number of students that had activity card = 125 - 83.47 = 41.53 ~ 42

Hence, nearly 42 students had an activity card.