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A box of cube candles — large and small
A candle maker packs a rectangular storage box tightly with 27 identical large cube-shaped candles and some identical small cube-shaped candles, so that candles of the same size are stacked directly on top of each other, filling the box exactly to the brim. The figure shows the first layer of candles packed in the box.
- (a) How many small candles does he have?
- (b) The volume of the box is 37800 cm³. The total volume of the 27 large candles is of the volume of the box. What is the length of one edge of the small candle?
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The pattern behind it: Repeated identity
One length or count, described two ways in the same question.
In this one. The figure gives no lengths — but two blocks spanning the same depth fix the edge ratio 5 : 3, and that ratio alone counts every candle; the volume is only needed at the very end.
How to spot it
A shape or count is described from two viewpoints in the same question, such as one edge measured as a number of long pieces and again as a number of short pieces.
Common mistake
Children treat the two descriptions as separate quantities and add them. Both describe the same quantity, so the two must be equal.
Try one like it
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All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
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