Three friends

Three friend squirrels together went to collect hazelnuts. Zrzecka found more than twice Pizizubka, and Ouska was even three times more than Pizizubka. On the way home, they talked while eating and cracked her nuts. Pizizubka ate half of all the nuts collected, Zrzecka a third of all its nuts, and Ouska a quarter of his own. At home, squirrels discovered that they were together and left 196 nuts. How many nuts are collected from each squirrel?

Correct answer:

o =  144
p =  48
z =  96

Step-by-step explanation:

z=2p
o=3p
(p-p/2)+(z-z/3)+(o-o/4)=196

z=2·p
o=3·p
(p-p/2)+(z-z/3)+(o-o/4)=196

2p-z = 0
o-3p = 0
9o+6p+8z = 2352

Pivot: Row 1 ↔ Row 3
9o+6p+8z = 2352
o-3p = 0
2p-z = 0

Row 2 - 1/9 · Row 1 → Row 2
9o+6p+8z = 2352
-3.667p-0.889z = -261.333
2p-z = 0

Row 3 - 2/-3.66666667 · Row 2 → Row 3
9o+6p+8z = 2352
-3.667p-0.889z = -261.333
-1.485z = -142.545


z = -142.54545455/-1.48484848 = 96
p = -261.33333333+0.88888888888889z/-3.66666667 = -261.33333333+0.88888889 · 96/-3.66666667 = 48
o = 2352-6p-8z/9 = 2352-6 · 48-8 · 96/9 = 144

o = 144
p = 48
z = 96

Our linear equations calculator calculates it.

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