Question

Jake, Sara, and Cole are selling tickets for the school drama show. Sara sells half as many tickets as Jake. Cole sells 6 more than twice as much as Jake. They sold a total of 538 tickets together.

a) Write an equation to represent the situation.
b) Solve to find how many tickets Sara sold.

Answer 1

Let x be the number of tickets Jake sold,

Since, Sara sells half as many tickets as Jake.

⇒ The ticket sold by Sara =
`(x)/(2)`

Also, Cole sells 6 more than twice as much as Jake.

⇒ The ticket sold by Cole = 2x + 6,

Thus, the ticket sold by all three =
`x+(x)/(2)+2x+6`

a) According to the question,

`x+(x)/(2)+2x+6=538`

b) By solving this equation,

`(2x+x+4x+12)/(2)=538`

`(7x+12)/(2)=538`

`7x+12=1076`

`7x=1064`

`\implies x=(1064)/(7)=152`

Thus, the number of tickets Sara has =
`(x)/(2)=(152)/(2)=76`

Answer 2

We let x be the number of tickets that Sara and Jake sold individually. With this representation, the number of tickets sold by Cole is equal to 2x+6.

(a) x + x + (2x + 6) = 538
The value of x from the generated equation is 133.

(b) Sara sold a total of 133 tickets.