Number sum

The sum of three numbers is 77. The largest is three times the smallest, and the middle number is half of the largest. Find all three numbers.

Final Answer:

a =  42
b =  21
c =  14

Step-by-step explanation:

$$\begin{gathered} a+b+c=77 \\ a=3c \\ b=a/2 \\ 3c+b+c=77 \\ 3c+a/2+c=77 \\ 3c+3c/2+c=77 \\ 3\cdot c+3\cdot c/2+c=77 \\ 11c=154 \\ c=\frac{154}{11}=14 \\ c=14 \\ a=3\cdot c=3\cdot 14=42 \end{gathered}$$

$b=a/2=42/2=21$

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