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

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