Chicken

I threw three chickens for a handful of grains, and I noticed that they ate in a ratio of 8:7:6, and two of them grabbed 156 grains. How many grains have fought that chicken?

Correct answer:

x =  96
y =  84
z =  72

Step-by-step explanation:


y+z =156; 7 x = 8 y; 6 y = 7 z

y+z =156
7·x = 8·y
6·y = 7·z

y+z = 156
7x-8y = 0
6y-7z = 0

Pivot: Row 1 ↔ Row 2
7x-8y = 0
y+z = 156
6y-7z = 0

Pivot: Row 2 ↔ Row 3
7x-8y = 0
6y-7z = 0
y+z = 156

Row 3 - 1/6 · Row 2 → Row 3
7x-8y = 0
6y-7z = 0
2.167z = 156


z = 156/2.16666667 = 72
y = 0+7z/6 = 0+7 · 72/6 = 84
x = 0+8y/7 = 0+8 · 84/7 = 96

x = 96
y = 84
z = 72

Our linear equations calculator calculates it.



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