Solving Inequalities and Weight Limits

The video tutorial addresses a problem involving an elevator's weight limit in a 10-story building. The task is to move boxes of books, each weighing 48 pounds, from the bottom to the sixth floor without exceeding the 1,400-pound limit. The tutorial defines variables, sets up an inequality, and solves it to determine the maximum number of boxes that can be moved per trip, considering the person's weight of 175 pounds. The solution shows that up to 25 boxes can be moved at once, ensuring the total weight does not exceed the limit.

What is the maximum weight the elevator can carry?

• 1,200 pounds

• 1,400 pounds

• 1,600 pounds

• 1,800 pounds

If each box weighs 48 pounds, what variable is used to represent the number of boxes?

• y

• n

• x

• b

What is the inequality that represents the weight limit problem?

• 175 + 48b > 1400

• 175 + 48b < 1400

• 175 + 48b ≤ 1400

• 175 + 48b = 1400

What is the first step in solving the inequality 175 + 48b ≤ 1400?

• Multiply both sides by 48

• Subtract 175 from both sides

• Divide both sides by 48

• Add 175 to both sides

After subtracting 175 from both sides, what is the resulting inequality?

• 48b ≤ 1225

• 48b ≥ 1225

• 48b = 1225

• 48b < 1225

What operation is performed to isolate the variable b in the inequality 48b ≤ 1225?

• Add 48

• Subtract 48

• Divide by 48

• Multiply by 48

What is the maximum number of boxes that can be moved in one trip?

• 25

• 27

• 24

• 26

Why can't the number of boxes be rounded up to 26?

• It would exceed the weight limit

• It would be too few boxes

• It would be too many trips

• It would be less than the weight limit

What must be true about the number of boxes, b, in the context of this problem?

• b must be greater than 50

• b must be a whole number

• b must be a fraction

• b must be negative

What is the significance of the remainder in the division process?

• It indicates an error

• It prevents exceeding the weight limit

• It allows rounding up

• It shows the exact number of boxes