Question

Xander goes to the movies with his soccer team. Each team member buys a ticket and two

boxes of popcorn. There are 13 team members.

Let t represent the cost of a ticket and p represent the cost of a box of popcorn.

a) Write two different expressions that represent the total amount the team spent.

b) Explain how each expression describes the situation in a different way.

Answer 1

Given that, the cost of a ticket = t and

cost of a box of popcorn = p.

Total members in the team = 13

As each team member buys 1 ticket and 2 boxes of popcorn, so, the amount spent by one member,
`C_1 = t+2p`

So, the total amount that the team spent
`= 13C_1`

(a) So, the first expression, representing the total amount spent by the team, is

`13* (t+2p)\cdots(i)`

On simplification, the second expression, representing the total amount spent by the team, is

`13*t + 13* (2p)`

`=13t+26p\cdots(ii)`

(b) The expression from the equation (i) represent the total amount spent as 13 times the expenses of one member, while equation (ii) is the sum of two terms where the first term, 13t, represents the total amount spent for buying the ticket and the second term, 26p, represents the total amount spent for buying popcorn