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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.

Respuesta :

taskmasters
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. 

Answer:

Let x be the number of tickets Jake sold,

Since, Sara sells half as many tickets as Jake.

⇒ The ticket sold by Sara = [tex]\frac{x}{2}[/tex]

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 = [tex]x+\frac{x}{2}+2x+6[/tex]

a) According to the question,

[tex]x+\frac{x}{2}+2x+6=538[/tex]

b) By solving this equation,

[tex]\frac{2x+x+4x+12}{2}=538[/tex]

[tex]\frac{7x+12}{2}=538[/tex]

[tex]7x+12=1076[/tex]

[tex]7x=1064[/tex]

[tex]\implies x=\frac{1064}{7}=152[/tex]

Thus, the number of tickets Sara has = [tex]\frac{x}{2}=\frac{152}{2}=76[/tex]