Vacation

Karel and his parents flew on vacation. When checking in at the airport, their 3 pieces of luggage had a total weight of 44 kg. Father's luggage weighed three times as much as Karl's luggage, and mother's luggage weighed half as much as father's luggage.
How many kilograms is mother's luggage heavier than Karl's luggage?

Correct answer:

x =  4 kg

Step-by-step explanation:


a+b+c = 44
a = 3b
c = a/2
x = c - b

a+b+c = 44
a = 3·b
c = a/2
x = c - b

a+b+c = 44
a-3b = 0
a-2c = 0
b-c+x = 0

Row 2 - Row 1 → Row 2
a+b+c = 44
-4b-c = -44
a-2c = 0
b-c+x = 0

Row 3 - Row 1 → Row 3
a+b+c = 44
-4b-c = -44
-b-3c = -44
b-c+x = 0

Row 3 - -1/-4 · Row 2 → Row 3
a+b+c = 44
-4b-c = -44
-2.75c = -33
b-c+x = 0

Row 4 - 1/-4 · Row 2 → Row 4
a+b+c = 44
-4b-c = -44
-2.75c = -33
-1.25c+x = -11

Row 4 - -1.25/-2.75 · Row 3 → Row 4
a+b+c = 44
-4b-c = -44
-2.75c = -33
x = 4


x = 4/1 = 4
c = -33/-2.75 = 12
b = -44+c/-4 = -44+12/-4 = 8
a = 44-b-c = 44-8-12 = 24

a = 24
b = 8
c = 12
x = 4

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