Final answer:
To calculate the lower bound for the mass of the books, we recognize that the total mass of box and books, which is 6 kg rounded to the nearest kilogram, must be at least 5.5 kg. Subtracting the minimum mass of the box, the books alone must weigh slightly less than 5.5 kg, indicating that 5 kg is the closest correct lower bound.
Step-by-step explanation:
The student has asked how to work out the lower bound for the mass of the books when the total mass of the box and the books is 6 kg, correct to the nearest kilogram. To solve this, we need to consider the concept of bounds in rounding. Since the total mass is given as 6 kg correct to the nearest kilogram, the lowest it could actually be is 5.5 kg because if it were any less, it would have been rounded down to 5 kg. This is because when rounding to the nearest kg, any mass from 5.5 kg (inclusive) to 6.4 kg (exclusive) would round to 6 kg. Now we need to subtract the minimum possible mass of the box. If the box had a non-zero mass, the books would have to weigh less than 5.5 kg. Therefore, the lower bound for the mass of the books alone would be slightly less than 5.5 kg, meaning option D, 5 kg, is the closest correct answer.