The receipts for one showing of a movie were $808 for an audience of 110 people. Children's tickets are $6, general admission is $8, and tickets for seniors are $7. Twice as many general admission tickets as children's tickets were purchased. If x is the number of children's tickets purchased, y is the number of general admissions tickets purchased, and z is the number of senior tickets purchased, write a system of three equations in three variables that models the situation.
A) $\left\{ \begin{array} { l }
x + y + z = 110 \
6 x + 8 y + 7 z = 808 \
y = 2 x
\end{array} \right.$
B) $\left\{ \begin{array} { l }
x + y + z = 110 \
6 x + 8 y + 7 z = 808 \
x = 2 y
\end{array} \right.$
C) $\left\{ \begin{array} { l }
x + y + z = 808 \
6 x + 8 y + 7 z = 110 \
y = 2 x
\end{array} \right.$
D) $\left\{ \begin{array} { l }
x + y + z = 808 \
6 x + 8 y + 7 z = 110 \
x = 2 y
\end{array} \right.$

Question

The receipts for one showing of a movie were $808 for an audience of 110 people. Children's tickets are $6, general admission is $8, and tickets for seniors are $7. Twice as many general admission tickets as children's tickets were purchased. If x is the number of children's tickets purchased, y is the number of general admissions tickets purchased, and z is the number of senior tickets purchased, write a system of three equations in three variables that models the situation.
A) $\left\{ \begin{array} { l } 
x + y + z = 110 \
6 x + 8 y + 7 z = 808 \
y = 2 x
\end{array} \right.$
B) $\left\{ \begin{array} { l } 
x + y + z = 110 \
6 x + 8 y + 7 z = 808 \
x = 2 y
\end{array} \right.$
C) $\left\{ \begin{array} { l } 
x + y + z = 808 \
6 x + 8 y + 7 z = 110 \
y = 2 x
\end{array} \right.$
D) $\left\{ \begin{array} { l } 
x + y + z = 808 \
6 x + 8 y + 7 z = 110 \
x = 2 y
\end{array} \right.$

Quizplus · Accepted Answer

The first equation represents the total number of tickets sold, the second equation represents the total revenue generated from those tickets, and the third equation represents the relationship between the number of general admission and children's tickets sold. These three equations accurately model the situation as described in the problem.

The Receipts for One Showing of a Movie Were $808 {x+y+z=1106x+8y+7z=808y=2x\left\{ \begin{array} { l } x + y + z = 110 \\6 x + 8 y + 7 z = 808 \\y = 2 x\end{array} \right.⎩⎨⎧​x+y+z=1106x+8y+7z=808y=2x​

The Receipts for One Showing of a Movie Were $808 $\left\{ \begin{array} { l } x + y + z = 110 \\6 x + 8 y + 7 z = 808 \\y = 2 x\end{array} \right.$