Number properties

Find four numbers whose sum is 48 and which have the following properties: if we subtract 3 from the first, add 3 to the second, multiply the third by three, and divide the fourth by three, we get the same result.

Final Answer:

a =  12
b =  6
c =  3
d =  27

Step-by-step explanation:

$$\begin{gathered} a+b+c+d=48 \\ a-3=b+3 \\ b+3=3c \\ 3c=d/3 \\ b=a-6 \\ c=b/3+1 \\ d=9c \\ a+b+c+d=48 \\ a+(a-6)+(b/3+1)+9c=48 \\ a+(a-6)+((a-6)/3+1)+9c=48 \\ a+(a-6)+((a-6)/3+1)+9((a-6)/3+1)=48 \\ a+(a-6)+((a-6)/3+1)+9\cdot ((a-6)/3+1)=48 \\ 16a=192 \\ a=\frac{192}{16}=12 \\ a=12 \end{gathered}$$

$b=a-6=12-6=6$

$c=b/3+1=6/3+1=3$

$d=9\cdot c=9\cdot 3=27$

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