Paper Reams Calculation Based on Copies and Sheets
This problem involves calculating the amount of paper required based on two variables: the number of copies and the number of sheets per book. We can use the concept of combined or joint variation (direct proportion).
Establishing the Relationship
The total number of sheets needed is directly proportional to both the number of copies and the number of sheets per book. Therefore, the number of reams required is also directly proportional to the product of copies and sheets.
Let R be the number of reams, C be the number of copies, and S be the number of sheets per book.
We can express this relationship as: $ R \propto C \times S $ Or, $ R = k \times C \times S $, where $ k $ is the constant of proportionality.
This leads to the formula: $ \frac{R_1}{C_1 \times S_1} = \frac{R_2}{C_2 \times S_2} $
Applying the Formula
We are given:
- $ C_1 = 100 $ copies
- $ S_1 = 15 $ sheets
- $ R_1 = 26 $ reams
- $ C_2 = 750 $ copies
- $ S_2 = 13 $ sheets
- We need to find $ R_2 $.
Substitute the known values into the formula:
$ \frac{26}{100 \times 15} = \frac{R_2}{750 \times 13} $Solving for the Unknown
Rearrange the equation to solve for $ R_2 $:
$ R_2 = 26 \times \frac{750 \times 13}{100 \times 15} $Simplify the expression:
$ R_2 = 26 \times \frac{750}{100} \times \frac{13}{15} $ $ R_2 = 26 \times 7.5 \times \frac{13}{15} $Alternatively, simplify by cancelling common factors:
$ R_2 = 26 \times \frac{750}{15} \times \frac{13}{100} $ $ R_2 = 26 \times 50 \times \frac{13}{100} $ $ R_2 = 26 \times \frac{650}{100} $ $ R_2 = 26 \times 6.5 $ $ R_2 = 169 $Conclusion
Therefore, 169 reams of paper are required for 750 copies of a book with 13 sheets.
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