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?

BilalKrol28282 Nov 19, 2023

#1**0 **

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

ThheBaIkanBeer Dec 20, 2023