Equation System for Tickets Sold

Hard Heart Of Algebra Linear Equations And Inequalities

In a local theater, the ticket pricing is structured such that the price for adult tickets is represented by the variable a, and the price for children's tickets is represented by the variable c. On a particular day, the theater sold a total of 150 tickets for $2,000. If the price of an adult ticket is $15 and the price of a children's ticket is $10, how can we express the relationship between adult and children's tickets sold?

Write a system of equations to effectively capture this situation.

$$ a + c = 150 $$ and $$ 15a + 10c = 2000 $$

$$ a + c = 2000 $$ and $$ 15a + 10c = 150 $$

$$ 15a + c = 150 $$ and $$ a + 10c = 2000 $$

$$ c + 10a = 150 $$ and $$ 10c + 15a = 2000 $$

Hint

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