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A movie theater showed an old, classic movie on Saturday and Sunday. Tickets cost [tex]c[/tex] dollars for children under the age of 13 and [tex]d[/tex] dollars for others.

On Saturday, they sold 84 children's tickets and 157 tickets for others, collecting $2,640 from ticket sales. On Sunday, they sold 67 children's tickets and 134 other tickets, collecting $2,211 from ticket sales. This can be represented by the following system of equations:

\[ 84c + 157d = 2,640 \]
\[ 67c + 134d = 2,211 \]

A. What could the equation [tex]17c + 23d = 429[/tex] mean in this situation?

B. The solution to the original system is the pair [tex]c = 9[/tex] and [tex]d = 12[/tex]. Explain why it makes sense that this pair of values is also a solution to the equation [tex]17c + 23d = 429[/tex].

Answer :

The equation in the given question is answered in main body.

What is equation?

In arithmetic , an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =

Main body:

according to question :

A) equation for Saturday sale = 84c +157d = 2640

equation for Sunday sale = 67c +134d = 2211

when subtracted we will get, 17c +23d = 429

This equation shows the difference in sales of these 2 days in terms of ticket sold and collection.

B) According to second part solution are c= 9 , d= 12.

equation given : 17c+23d = 429

now substituting value of c and d.

⇒17(9) + 23(12)

⇒153+276

⇒429 = R.H.S

Hence equation satisfies.

to know more about equation click on the link below

https://brainly.com/question/22688504

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