How much does the pen weigh?

Question

Priya is playing around with a two-plate scale and finds that the
scale stays in equilibrium if one plate is filled with two keys,
two coins and three toy soldiers OR one apple, one toy soldier and
one lemon, and the other plate with a weight of 100 grams. One
coin, one key, one soldier and one plum together weigh 50 grams.
The lemon, the apple and the plum weigh exactly the same as one
coin, one key, one soldier and one pen.

How much does the pen weigh?

Answer 1

50 g

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Lets simplify definitions: Key-k, Coin- c, Toy Soldier- s, Apple- a, Lemon- l, Plum- pl, pen- p
We have:
2k+2c+3s=1a+1s+1l=100 g----> (1)
1k+1c+1s+1pl=50 g -----> (2)
1l+1a+1pl=1c+1k+1s+1p----> (3)
1p=?

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From (1) & (2), 2k+2c+2s=100-1s & 2k+2c+2s=100-2pl => 1s=2pl
From (2) & (3), 1l+1a+1pl=50-1pl+1p => 1l+1a+2pl=50+1p => 1l+1a+1s=50+1p => 100=50+1p => 1p=50 g
1p=50 g