Electricity bill - share

Three roommates divided the electricity bill according to the time spent on the PC. Adam and Brano's time is divided in the ratio of 1:4, and Brano and Damian's time is divided in the ratio of 2:5.
In what proportion do all three boys spend the time at the PC?
How much will Adam pay if they pay 30 euros a month together?

Correct answer:

r = 1:4:10
a =  2 eur

Step-by-step explanation:

$$\begin{gathered} a:b=1:4 \\ b:d=2:5 \\ 4=2^2 \\ 2...\text{ prime number} \\ LCM(4,2)=2^2=4 \\ w=LCM(4,2)=4 \\ 1:4=1:4 \\ 2:5=4:10 \\ r=a:b:d \\ r=1:4:10 \end{gathered}$$

$$\begin{gathered} s=30 \\ a=s\cdot \frac{1}{1+4+10}=30\cdot \frac{1}{1+4+10}=2\text{eur} \end{gathered}$$

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