Paint usage calculation

The painter used 3.5 times more paint to paint the tin roof than the gutters. He used 3.1 kg more paint to paint the gutters than to paint the fence. In total, he used 20 kg of paint. How many kilograms of paint did he use to grease the roof, fence, and gutters?

Final Answer:

p =  1.1
s =  14.7
z =  4.2

Step-by-step explanation:


s = 3.5 z
z = p + 3.1
s+p+z = 20

s = 3.5·z
z = p + 3.1
s+p+z = 20

s-3.5z = 0
p-z = -3.1
p+s+z = 20

Pivot: Row 1 ↔ Row 3
p+s+z = 20
p-z = -3.1
s-3.5z = 0

Row 2 - 1 · Row 1 → Row 2
p+s+z = 20
-s-2z = -23.1
s-3.5z = 0

Pivot: Row 2 ↔ Row 3
p+s+z = 20
s-3.5z = 0
-s-2z = -23.1

Row 3 - -1 · Row 2 → Row 3
p+s+z = 20
s-3.5z = 0
-5.5z = -23.1


z = -23.1/-5.5 = 4.2
s = 0+3.5z = 0+3.5 · 4.2 = 14.7
p = 20-s-z = 20-14.7-4.2 = 1.1

p = 11/10 = 1.1
s = 147/10 = 14.7
z = 21/5 = 4.2

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