Three unknown numbers

The sum of the three numbers is 106. the first number is ten more than the third. The second number is 2x the third. What are the numbers?

Correct answer:

a =  34
b =  48
c =  24

Step-by-step explanation:


a+b+c=106
a=10+c
b=2·c

a+b+c = 106
a-c = 10
b-2c = 0

Row 2 - Row 1 → Row 2
a+b+c = 106
-b-2c = -96
b-2c = 0

Row 3 + Row 2 → Row 3
a+b+c = 106
-b-2c = -96
-4c = -96


c = -96/-4 = 24
b = -96+2c/-1 = -96+2 · 24/-1 = 48
a = 106-b-c = 106-48-24 = 34

a = 34
b = 48
c = 24

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