Gasoline canisters

Thirty-five liters of gasoline is to be divided into four canisters so that the third canister will have 5 liters less than the first canister, the fourth canister 10 liters more than the third canister, and the second canister half of that in the first canister. How many liters of gasoline are in each canister?

Correct answer:

a =  10
b =  5
c =  5
d =  15

Step-by-step explanation:


a+b+c+d=35
c = a-5
d = 10 +c
b = a/2

a+b+c+d = 35
a-c = 5
c-d = -10
a-2b = 0

Row 2 - Row 1 → Row 2
a+b+c+d = 35
-b-2c-d = -30
c-d = -10
a-2b = 0

Row 4 - Row 1 → Row 4
a+b+c+d = 35
-b-2c-d = -30
c-d = -10
-3b-c-d = -35

Pivot: Row 2 ↔ Row 4
a+b+c+d = 35
-3b-c-d = -35
c-d = -10
-b-2c-d = -30

Row 4 - -1/-3 · Row 2 → Row 4
a+b+c+d = 35
-3b-c-d = -35
c-d = -10
-1.6667c-0.6667d = -18.3333

Pivot: Row 3 ↔ Row 4
a+b+c+d = 35
-3b-c-d = -35
-1.6667c-0.6667d = -18.3333
c-d = -10

Row 4 - 1/-1.66666667 · Row 3 → Row 4
a+b+c+d = 35
-3b-c-d = -35
-1.6667c-0.6667d = -18.3333
-1.4d = -21


d = -21/-1.4 = 15
c = -18.33333333+0.66666666666667d/-1.66666667 = -18.33333333+0.66666667 · 15/-1.66666667 = 5
b = -35+c+d/-3 = -35+5+15/-3 = 5
a = 35-b-c-d = 35-5-5-15 = 10

a = 10
b = 5
c = 5
d = 15

Our linear equations calculator calculates it.



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 looking for calculator system of linear equations?
Tip: Our volume units converter will help you convert volume units.

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: