Question
make 3 hard inequalities word problems
Answers
GPT-4o mini
Here are three challenging inequalities word problems:
### Problem 1: Crop Yield
A farmer has two fields, Field A and Field B. Field A produces twice as much corn per acre as Field B. Last year, Field B produced at least 150 bushels of corn per acre. This year, the farmer plans to plant a combined total of more than 80 acres in both fields. Let \( x \) represent the number of acres planted in Field B. Write an inequality to represent the minimum amount of corn (in bushels) that should be produced this year. Then, find a range of possible values for \( x \).
### Problem 2: Budget Constraints
A student has a weekly budget of $150 for food and entertainment. The cost of food each week is represented by \( f \) and is known to be at least $50. The student spends at least 3 times as much on entertainment as on food. Set up an inequality that represents the student's budget constraint, and find the range of possible values for the spending on entertainment.
### Problem 3: Travel Distance
Maria is planning a road trip and can drive a maximum of 480 miles in one day. She wants to divide her trip into two segments: the first segment to the city of Springfield and the second segment to the city of Lincoln. Maria plans to travel at a speed of at least 60 miles per hour and wants to spend no more than 10 hours driving in total. Let \( x \) represent the distance to Springfield and \( y \) represent the distance to Lincoln. Write an inequality to represent the distance Maria can drive to both cities, then determine a suitable range for \( x \) if the distance to Lincoln \( y \) is less than or equal to 200 miles.
### Solutions
Feel free to attempt solving these problems, and I can provide guidance or solutions if needed!
### Problem 1: Crop Yield
A farmer has two fields, Field A and Field B. Field A produces twice as much corn per acre as Field B. Last year, Field B produced at least 150 bushels of corn per acre. This year, the farmer plans to plant a combined total of more than 80 acres in both fields. Let \( x \) represent the number of acres planted in Field B. Write an inequality to represent the minimum amount of corn (in bushels) that should be produced this year. Then, find a range of possible values for \( x \).
### Problem 2: Budget Constraints
A student has a weekly budget of $150 for food and entertainment. The cost of food each week is represented by \( f \) and is known to be at least $50. The student spends at least 3 times as much on entertainment as on food. Set up an inequality that represents the student's budget constraint, and find the range of possible values for the spending on entertainment.
### Problem 3: Travel Distance
Maria is planning a road trip and can drive a maximum of 480 miles in one day. She wants to divide her trip into two segments: the first segment to the city of Springfield and the second segment to the city of Lincoln. Maria plans to travel at a speed of at least 60 miles per hour and wants to spend no more than 10 hours driving in total. Let \( x \) represent the distance to Springfield and \( y \) represent the distance to Lincoln. Write an inequality to represent the distance Maria can drive to both cities, then determine a suitable range for \( x \) if the distance to Lincoln \( y \) is less than or equal to 200 miles.
### Solutions
Feel free to attempt solving these problems, and I can provide guidance or solutions if needed!