Gasoline

35 l of gasoline is to be divided into four canisters so that in the third canister was 5 l less than the first canister, the fourth canister 10 l more than in the third canister, and the second canister half what in the first canister. How many liters of fuel are in each canister?

Correct answer:

a =  10 l
b =  5 l
c =  5 l
d =  15 l

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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