Question

A briefcase with 5 magazines in it has a mass of 2.58 kg. When 6 more magazines and 22 guide books are added, the mass becomes 4.28 kg. Each magazine has a mass 2 times as much as each guide book. Find the mass of the briefcase when it is empty. Express the answer in kg.

Answer 1

each guide book : x kg
each magazine : 2x kg
empty briefcase : y kg
2x * 5 + y = 2.58
2.58 + 6.2x + 22 * x = 4.28

x = 0.05
y = 2.08

2.08 kg

Answer 2

If the guide book has mass x, and the briefcase has mass b, then
2x*5 + b = 2.58
2x*(5+6) + x*22 + b = 4.28
But, since b = 2.58-10x, that gives
22x + 22x + 2.58-10x = 4.28
x = 0.141 kg
That makes the briefcase weigh 2.58 - 1.41 = 1.17 kg