Certainly! Below are some math questions based on a story that involves inequalities. Let's create a fictional scenario and then derive questions from it.
Story:
Lisa and Mark are selling cookies at their school bake sale. Lisa makes chocolate chip cookies and Mark makes oatmeal cookies. They decide that they want to raise at least $50 to donate to charity. Each chocolate chip cookie sells for $2, while each oatmeal cookie sells for $3. Together, they have made a total of 30 cookies.
Questions:
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Cookie Count Inequality: Let \( x \) represent the number of chocolate chip cookies and \( y \) represent the number of oatmeal cookies. Write an inequality that represents the total number of cookies made by Lisa and Mark.
Answer: \( x + y \leq 30 \)
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Revenue Inequality: Write an inequality that represents the total amount of money raised by selling these cookies, where the goal is to raise at least $50.
Answer: \( 2x + 3y \geq 50 \)
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Maximum Number of Oatmeal Cookies: If Lisa is determined to make at least 10 chocolate chip cookies, how many oatmeal cookies can Mark make at most?
Answer: Substituting \( x \geq 10 \) into \( x + y \leq 30 \): \( 10 + y \leq 30 \) leads to \( y \leq 20 \).
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Minimum Quantity of Cookies Needed for Goal: If Mark only makes oatmeal cookies (i.e., \( x = 0 \)), how many oatmeal cookies must he sell to reach their goal of $50?
Answer: Using the inequality \( 3y \geq 50 \): \( y \geq \frac{50}{3} \approx 16.67 \). Since he can only make whole cookies, he needs to sell at least 17 oatmeal cookies.
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Combination of Cookies: If Lisa makes 15 chocolate chip cookies, how many oatmeal cookies must Mark make in order to still meet the goal of raising at least $50?
Answer: With \( x = 15 \): Using the currency inequality: \( 2(15) + 3y \geq 50 \) \( 30 + 3y \geq 50 \) leads to \( 3y \geq 20 \), hence \( y \geq \frac{20}{3} \approx 6.67 \). Mark needs to make at least 7 oatmeal cookies.
Summary:
These questions based on the fictional scenario utilize inequalities to challenge students in a practical context involving math. Each question progresses in difficulty and requires critical thinking about the relationships between the quantities involved.