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 on the gutters than on the fence. In total, he used 20 kg of paint. How many kilograms of paint did he use on the roof, the fence, and the 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

Our linear equations calculator calculates it.



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