Question
make questions for math thew sotry with the inequality
Answers
GPT-4o mini
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:
1. **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:**
\( x + y \leq 30 \)
2. **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:**
\( 2x + 3y \geq 50 \)
3. **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 \( y \leq 20 \).
4. **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.
5. **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.
### 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:
1. **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:**
\( x + y \leq 30 \)
2. **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:**
\( 2x + 3y \geq 50 \)
3. **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 \( y \leq 20 \).
4. **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.
5. **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.