Use a system of linear equations in three variables to solve the following probl

Question

Use a system of linear equations in three variables to solve the following problem. At a college production of a play, 300 tickets were sold. The ticket prices were $8, $10, and $12, and the total income from ticket sales was $2700. How many tickets of each type were sold if the combined number of $8 and $10 tickets sold was 5 times the number of $12 tickets sold? Write a system of linear equations using the given information. Choose correct answer below. A. {x + y + z = 2700 8x + 10y + 12z = 300 x + y + 5z = 0 B. {x + y + z = 300 8x + 10y + 12z = 2700 x + y - 5z = 0 C. {x + y + z = 2700 8x + 10y + 12x = 300 x + y - 5z = 0 D. {x + y + z = 300 8x + 10y + 12z = 2700 x + y + 5z = 0

Explanation / Answer

let 8$ ticket is x

10$ ---------y

12$ ---------------z   

three tickets TOTAL 300

x+y+z=300

condition is sum of 8$ and 10$ tickets are 5times of 12$ tickets

x+y=5z

x+y-5z=0

and income is 8X+10y+12z=2700

answer is option B)

solving above equations we get

x=200 (8$ tickets)

y=50 ( 10$ tickets)

z=50 (12$ tickets)

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