Kilograms 5738

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?

Correct 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.

Try another example


Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Do you have a system of equations and are looking for calculator system of linear equations?

You need to know the following knowledge to solve this word math problem:

Units of physical quantities:

Grade of the word problem:

Related math problems and questions: