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primary 6 | Maths
| Data Analysis
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How to find, where to start first???
Since you're told the mass of one screw is twice of a nail, it just means 1 screw weighs the same as 2 nails.
40 × 2 = 80
40 screws will have the same mass as 80 nails.
So, the jar with 40 screws has the same mass as a jar with 80 nails.
It's like you replace the 40 screws with 80 nails and the mass stays the same.
Now compare this to the jar with only 20 nails.
First, convert 1.4kg to 1400g.
Then,
Difference in mass = 1400g - 500g = 900g
But difference also = 80 nails - 20 nails = 60 nails
This tells you that 60 nails weigh 900g.
Since we need the mass of 20 nails only, and 60 ÷ 3 = 20,
Mass of 20 nails = 900g ÷ 3 = 300g
Mass of jar = 500g - 300g = 200g
The jar with 20 nails weighs the same as a jar with 10 screws, since 20 nails has the same mass as 10 screws.
Compare this to the first jar,
Difference in mass = 1400g - 500g = 900g
But difference also = 40 screws - 10 screws
= 30 screws
Mass of 30 screws = 900g
So mass of 10 screws = 900g ÷ 3 = 300g
Mass of empty jar = 500g - 300g = 200g
Or, if you use the first jar to find,
Mass of 40 screws = 300g × 4 = 1200g
Mass of empty jar = 1400g - 1200g = 200g
There is no need to use algebra or models at all.
There is also no need to find the mass of a single screw or nail first (though you can do so if you want, it is 15g per nail and 30g per screw)