Answer: B. x + y + z = 11
2x + 3y + 2z = 27
x + 2y + 2z = 19
C. x + y + z = 11
Step-by-step explanation:
Let x represent the number of dramas that each of them chose.
Let y represent the number of comedies that each of them chose.
Let z represent the number of documentaries that each of them chose.
Gina chose 11 movies total. This means that
x + y + z = 11 - - - - - - - - - - - 1
Sam chose twice as many dramas, three times as many comedies, and twice as many documentaries as Gina. He chose 27 movies total. This means that
2x + 3y + 2z = 27 - - - - - - - - - - - 2
Robby chose 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina. This means that
x + 2x + 2y = 19 - - - - - - - - - - - 3
equations 1,2 and 3represents their movie choices.
B.
[tex]x + y + z = 11\\2x + 3y + 2z = 27\\x + 2y + 2z = 19[/tex]
A set of simultaneous equations is a finite collection of equations for which common solutions are sought, often known as a system of equations or an equation system.
Suppose Gina chose [tex]\boldsymbol{x}[/tex] dramas, [tex]\boldsymbol{y}[/tex] comedies, and [tex]\boldsymbol{z}[/tex] documentaries.
As Gina chose 11 movies total,
[tex]\boldsymbol{x+y+z=11}[/tex]
Sam chose twice as many dramas, three times as many comedies, and twice as many documentaries as Gina. Also, he chose 27 movies total.
[tex]\boldsymbol{2x+3y+2z=27}[/tex]
Robby chose 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina.
[tex]\boldsymbol{x+2y+2z=19}[/tex]
System of equations is as follows:
B.
[tex]x + y + z = 11\\2x + 3y + 2z = 27\\x + 2y + 2z = 19[/tex]
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