Question

Arjun purchased 5 tickets to a play, each with the same price. He was also charged an online service fee of $3.50 per ticket. Emilia purchased 3 tickets to the same play and paid twice as much for her tickets as Arjun. Emilia was also charged a service fee of $2.75 per ticket. If they spent the same amount, choose the response that gives an equation that represents the situation and then gives the cost of each of the tickets Arjun purchased? Let t represent the cost of each of Arjun's tickets. Multiple choice question. Cross out A) 5t+3.5=(3)2t+2.75 , Each ticket costs $6.25. Cross out B) 6(t+3.5)=4(t+2.75) , Each ticket costs $5.00. Cross out C) 5(t+3.5)=3(2t+2.75) , Each ticket costs $9.75. Cross out D) 5(t+2.75)=3(2t+3.5) , Each ticket costs $3.25.

Answer 1

Answer: C) 5(t+3.5)=3(2t+2.75) , Each ticket costs $9.25.

Explanation:

Let t=cost of each of Arjun's tickets.

Arjun bought 5 tickets, he was charged an online service fee of $3.50 per ticket.

Total cost for Arjun = 5 (t+3.50)

As Emilia paid twice as Arjun, cost per ticket for Emilia = 2t

She bought 3 tickets and charged a service fee of $2.75 per ticket.

Total cost for Emilia = 3(2t+2.75)

If they same amount then

`5 (t+3.50)= 3(2t+2.75)\\\\\Rightarrow\ 5t+17.5=6t+8.25\\\\\Rightarrow 17.5-8.25=6t-5t\\\\\Rightarrow 9.25 =t\\\\\Rightarrow t=9.25`

Hence, cost of each of Arjun's tickets = $9.25

Hence, the correct option is (C).