Question

Gina, Sam, and Robby all chose movies they would like to see over the next year. They each chose some dramas, comedies, and documentaries. Gina chose 11 movies total. Sam chose twice as many dramas, three times as many comedies, and twice as many documentaries as Gina. He chose 27 movies total. Robby chose 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina. Which system of equations represents their movie choices?
A. x + y + z = 11
2x + 2y + 3z = 27
x + 2y + 2z = 19
B. x + y + z = 11
2x + 3y + 2z = 27
x + 2y + 2z = 19
C. x + y + z = 11
2x + 3y + 2z = 27
2x + 3y + 3z = 19
D. x + y + z = 11
3x + 2y + 2z = 27
x + 2y + 2z = 19

Answer 1

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.

Answer 2

B.

$x + y + z = 11\\2x + 3y + 2z = 27\\x + 2y + 2z = 19$

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 $\boldsymbol{x}$ dramas, $\boldsymbol{y}$ comedies, and $\boldsymbol{z}$ documentaries.

As Gina chose 11 movies total,

$\boldsymbol{x+y+z=11}$

Sam chose twice as many dramas, three times as many comedies, and twice as many documentaries as Gina. Also, he chose 27 movies total.

$\boldsymbol{2x+3y+2z=27}$

Robby chose 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina.

$\boldsymbol{x+2y+2z=19}$

System of equations is as follows:

B.

$x + y + z = 11\\2x + 3y + 2z = 27\\x + 2y + 2z = 19$

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