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2. One night Amc sold 548 movie tickets. AN adult’s ticket costs $13 and a child’s ticket costs $7. That night the movie theater made $5762. How many adult tickets were sold and how many children's tickets were sold? Define Variables:System of Equations:Answer as a sentence:

Respuesta :

Solution

Let the number of adult tickets be A

Let the number of child's tickets be C

Since Amc sold 548 movie tickets.

A + C = 548 ------(1)

Also, if an adult’s ticket costs $13 and a child’s ticket costs $7 and the movie theater made $5762,

=> 13A + 7C = 5762 -----(2)

solving equations (1) and (2) simultaneously,

[tex]A=548-C\text{ -----(3)}[/tex]

Substituting 548 - C for A in equation (2)

[tex]\begin{gathered} \Rightarrow13(548-C)+7C=5762 \\ \\ \Rightarrow7124-13C+7C=5762 \\ \\ \Rightarrow7124-5762=13C-7C \\ \\ \Rightarrow1362=6C \\ \\ \Rightarrow C=\frac{1362}{6}=227 \\ \\ \Rightarrow A=548-227=321 \end{gathered}[/tex]

There are 321 adult tickets being sold and 227 children's tickets were sold.

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