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A box contains 15 identical reams of paper. The total mass of the box with 1/5 of all the reams of papers is 33.6 kg lighter than the box with al the reams of paper. The mass of the empty box is 2/7 of a ream of paper. What is the mass of the empty box?

 Nov 19, 2023
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p = mass of one ream of paper in kg
(2/7)p = mass of the empty box in kg

A = mass of empty box and 3 reams of paper
A = (2/7)p + 3p 
A = (2/7 + 3)p 
A = (2/7 + 21/7)p 
A = (23/7)p 
Note that 3 reams is 1/5 of the total 15 reams.

B = mass of empty box and 15 reams of paper
B = (2/7)p + 15p 
B = (2/7 + 15)p 
B = (2/7 + 105/7)p 
B = (107/7)p 

Mass A is 33.6 kg lighter compared to mass B.
A = B - 33.6
(23/7)p = (107/7)p - 33.6
7*(23/7)p = 7*( (107/7)p - 33.6 )
23p = 107p - 235.2
23p-107p = -235.2
-84p = -235.2
p = -235.2/(-84)
p = 2.8
Each ream of paper has a mass of 2.8 kg.

(2/7)*p = (2/7)*2.8 = 0.8 kg is the mass of the empty box.

Notes:
2.8 = 14/5
0.8 = 4/5

 Dec 20, 2023

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