A set of dictionaries which fitted exactly 4 shelves, each 2.05 m long, was replaced by a new set. Every 7 old dictionaries was replaced by 4 new ones, each 5 cm thick. If the new set of dictionaries also fitted the 4 shelves exactly, what was the difference in the number of dictionaries between the two sets? [SCGS 2009 P6 SA1 P2 Q17]
A set of dictionaries which fitted exactly 4 shelves, each 2.05 m long.
A set of dictionaries which fitted exactly 4 shelves, each 2.05 m long.
Firstly, find the total length of the 4 shelves.
4 x 2.05 = 8.20 m = 820 cm Always good to show the conversion.
4 new ones, each 5 cm thick.
Next, find the thickness of 4 new dictionaries.
4 new ones, each 5 cm thick.
Next, find the thickness of 4 new dictionaries.
4 x 5 = 20 cm
Find the number of groups of dictionaries. [There is no need to find the number of new and old dictionaries.]
820 ÷ 20 = 41 groups
820 ÷ 20 = 41 groups
Every 7 old dictionaries was replaced by 4 new ones.
Make use of the difference in one group (7 – 4) to find the total difference in 41 groups.
1 group --> 7 – 4 = 3
41 groups -- > 41 x 3 = 123
The difference in the number of dictionaries between the 2 sets is 123.
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