Same pattern as Chairs — rearranged into rows of 7. New numbers, new
story. Try each one on paper, then check the working below — or watch it drawn out, the
same way the problem above is.
Question 1
In a library, books were arranged on shelves with exactly 8 books on each shelf. The librarian brought 4 more books into the library and rearranged all the books. There are now exactly 6 books on each shelf and 10 more shelves than before. How many books are there in the library now?
In a garden nursery, flower pots were arranged in rows with exactly 15 pots in each row. The gardener bought 10 more pots and rearranged all the pots. There are now exactly 10 pots in each row and 8 more rows than before. How many flower pots are there in the nursery now?
The extra shelves each hold 6 books, so find how many books those extra shelves hold in total.10 × 6 = 60
Only 4 new books were brought in, so the rest of those books must have come from the old shelves.60 − 4 = 56
Work out how many books each old shelf lost when it was rearranged.8 − 6 = 2
Divide the books taken from the old shelves by the loss per shelf to find the original number of shelves.56 ÷ 2 = 28
Multiply the original number of shelves by the original books per shelf to find the original total.28 × 8 = 224
Add the 4 new books to get the total number of books now.224 + 4 = 228
There are 228 books in the library now.
The pattern. Gap and difference: the extra shelves' capacity minus the books actually added gives what was pulled from old shelves, and dividing by the per-shelf drop fixes the original number of shelves.
The extra rows each hold 10 pots, so find how many pots those extra rows hold in total.8 × 10 = 80
Only 10 new pots were bought, so the rest of those pots must have come from the old rows.80 − 10 = 70
Work out how many pots each old row lost when it was rearranged.15 − 10 = 5
Divide the pots taken from the old rows by the loss per row to find the original number of rows.70 ÷ 5 = 14
Multiply the original number of rows by the original pots per row to find the original total.14 × 15 = 210
Add the 10 new pots to get the total number of pots now.210 + 10 = 220
There are 220 flower pots in the nursery now.
The pattern. Gap and difference: the extra rows' capacity minus the pots actually added gives what was pulled from old rows, and dividing by the per-row drop fixes the original number of rows.