To find out how many books weighing \(1 \frac{7}{8}\) kilograms can fit in a box that holds \(28 \frac{1}{8}\) kilograms, we need to first convert the mixed numbers to improper fractions or decimals.
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Convert \(28 \frac{1}{8}\) 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 \(1 \frac{7}{8}\) to an improper fraction: \[ 1 \frac{7}{8} = \frac{1 \times 8 + 7}{8} = \frac{8 + 7}{8} = \frac{15}{8} \]
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Now, divide the total weight the box can hold by the weight of one book: \[ \text{Number of books} = \frac{28 \frac{1}{8}}{1 \frac{7}{8}} = \frac{\frac{225}{8}}{\frac{15}{8}} = \frac{225}{8} \times \frac{8}{15} = \frac{225}{15} = 15 \]
So, the box can hold 15 books weighing \(1 \frac{7}{8}\) kilograms each.