Three numbers

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

Final Answer:

a =  3
b =  4
c =  8

Step-by-step explanation:

$$\begin{gathered} a=1/A \\ b=1/B \\ c=1/C \\ A+B=7/12 \\ A+C=11/24 \\ B+C=3/8 \\ (7/12-B)+C=11/24 \\ B+C=3/8 \\ 24B-24C=3 \\ 8B+8C=3 \\ Row2-\frac{8}{24}\cdot Row1\to Row2 \\ 16C=2 \\ C=\frac{2}{16}=0.125 \\ B=\frac{3+24C}{24}=\frac{3+24\cdot 0.125}{24}=0.25 \\ B=\frac{1}{4}=0.25 \\ C=\frac{1}{8}=0.125 \\ A=7/12-B=7/12-0.25=\frac{1}{3}\doteq 0.3333 \\ a=1/A=1/0.3333=3 \end{gathered}$$

$b=1/B=1/0.25=4$

$c=1/C=1/0.125=8$

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