Collected 4815

Pupils collected a total of 42 kg of apples. Peter harvests half as much as Zuzka and Martin, a third less than Petr. How much did each of them harvest?

Correct answer:

m =  12
p =  18
z =  12

Step-by-step explanation:


p+z+m=42
p = 1.5 z
m = p - p/3

p+z+m=42
p = 1.5·z
m = p - p/3

m+p+z = 42
p-1.5z = 0
3m-2p = 0

Pivot: Row 1 ↔ Row 3
3m-2p = 0
p-1.5z = 0
m+p+z = 42

Row 3 - 1/3 · Row 1 → Row 3
3m-2p = 0
p-1.5z = 0
1.667p+z = 42

Pivot: Row 2 ↔ Row 3
3m-2p = 0
1.667p+z = 42
p-1.5z = 0

Row 3 - 1/1.66666667 · Row 2 → Row 3
3m-2p = 0
1.667p+z = 42
-2.1z = -25.2


z = -25.2/-2.1 = 12
p = 42-z/1.66666667 = 42-12/1.66666667 = 18
m = 0+2p/3 = 0+2 · 18/3 = 12

m = 12
p = 18
z = 12

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