Nina has a gift card for $40 to a movie theater. The theater offers $6 afternoon movies and $11 evening movies. Enter an inequality to represent the number of afternoon movies x an... Nina has a gift card for $40 to a movie theater. The theater offers $6 afternoon movies and $11 evening movies. Enter an inequality to represent the number of afternoon movies x and the number of evening movies y Nina can attend using only her gift card.
Understand the Problem
The question is asking for an inequality that represents the relationship between the number of afternoon movies (x) Nina can attend and the number of evening movies (y) she can attend using a gift card of $40, with the costs of the movies specified. This requires creating an equation based on her budget.
Answer
$$ 6x + 11y \leq 40 $$
Answer for screen readers
The inequality is given by: $$ 6x + 11y \leq 40 $$
Steps to Solve
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Define the costs The cost of an afternoon movie is $6, and the cost of an evening movie is $11.
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Set up the equation based on her budget Nina has a gift card for $40, so we can set up the equation: $$ 6x + 11y \leq 40 $$ Here, $x$ represents the number of afternoon movies, and $y$ represents the number of evening movies.
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Write the inequality The inequality that represents the relationship is: $$ 6x + 11y \leq 40 $$
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Interpret the inequality This inequality means that the total cost of the movies Nina chooses (afternoon and evening) cannot exceed $40.
The inequality is given by: $$ 6x + 11y \leq 40 $$
More Information
This inequality helps to determine all possible combinations of afternoon and evening movies that Nina can watch without exceeding her budget of $40. The solution set will consist of all ordered pairs ((x, y)) that satisfy this condition.
Tips
- Confusing the total amount available with the costs of the individual movies.
- Forgetting to include the inequality sign when forming the equation.
- Incorrectly calculating the total amounts if more than two types of movies or costs are considered.
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