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!
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