Subjects algebra

Shelf Files

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1. **State the problem:** Jack's shelf can hold either 42 files or 36 stamp albums. He placed 18 files and 18 stamp albums on the shelf. We need to find how many more files can fit on the shelf. 2. **Understand the problem:** The shelf capacity is given in terms of files or stamp albums separately. We need to find the remaining space in terms of files after placing 18 files and 18 stamp albums. 3. **Calculate the space taken by 18 stamp albums in terms of files:** Since 42 files fit the shelf and 36 stamp albums fit the shelf, 1 stamp album equals $$\frac{42}{36} = \frac{7}{6}$$ files. So, 18 stamp albums take $$18 \times \frac{7}{6} = 21$$ files worth of space. 4. **Calculate total space used:** Files used: 18 files Stamp albums space in files: 21 files Total space used: $$18 + 21 = 39$$ files worth of space. 5. **Calculate remaining space for files:** Shelf capacity in files: 42 files Remaining space: $$42 - 39 = 3$$ files 6. **Answer:** Jack can fit at most **3 more files** on the shelf. --- **Second problem (not solved as per instructions):** Bakery sold 58 eclairs in the morning and 15 fewer in the afternoon. Total eclairs sold = ? --- Final answer for the first problem: **3 more files** can fit on the shelf.