Three numbers

What is three numbers which have the property: the sum of the reciprocals of the first and second numbers is 12/7, the first and third 11/24 and the second and the third 3/8.

Correct result:

a =  3
b =  4
c =  8

Solution:

$a = 1/A \ \\ b = 1/B \ \\ c = 1/C$

A+B = 7/12
A+C = 11/24
B+C = 3/8

12A+12B = 7
24A+24C = 11
8B+8C = 3

A = 1/3 ≈ 0.333333
B = 1/4 = 0.25
C = 1/8 = 0.125

Our linear equations calculator calculates it.

$a = 1/A = 1/(1/3) = 3 \ \\ b = 1/B = 1/(1/4) = 4$

$c=1/(1/8)=8$

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