To determine how many books weighing 1 7/8 kilograms each can fit into a box that can hold 28 1/8 kilograms, we need to divide the total weight capacity of the box by the weight of each book.
First, we convert the mixed numbers to improper fractions:
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Convert 28 1/8 to an improper fraction: \[ 28 \frac{1}{8} = \frac{28 \times 8 + 1}{8} = \frac{224 + 1}{8} = \frac{225}{8} \]
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Convert 1 7/8 to an improper fraction: \[ 1 \frac{7}{8} = \frac{1 \times 8 + 7}{8} = \frac{8 + 7}{8} = \frac{15}{8} \]
Now, we divide the total weight capacity of the box by the weight of one book: \[ \text{Number of books} = \frac{\frac{225}{8}}{\frac{15}{8}} = \frac{225}{8} \times \frac{8}{15} = \frac{225}{15} = 15 \]
Thus, the box can hold 15 books that each weigh 1 7/8 kilograms.