Hotel star distribution

There are several hotels in the Sunny Beach resort. Among them are one-, two-, three- and four-star hotels. During the walk, Jane calculated that the sum of all the stars in the resort was 69. More than half of the stars belong to one-star hotels. The number of three-star hotels is three times larger than the number of four-star hotels. Two-star hotels are less than three-star. How many hotels in the resort can have two stars?

Final Answer:

d = 0...3

Step-by-step explanation:

$$\begin{gathered} 69=1a+2b+3c+4d \\ 3c=d \\ b<c \\ a{\ge }_0 \\ b{\ge }_0 \\ c{\ge }_0 \\ d{\ge }_0 \\ {a}_1=3,b_1=3,c_1=4,d_1=12 \\ {a}_2=5,b_2=2,c_2=4,d_2=12 \\ {a}_3=7,b_3=1,c_3=4,d_3=12 \\ {a}_4=9,b_4=0,c_4=4,d_4=12 \\ {a}_5=20,b_5=2,c_5=3,d_5=9 \\ {a}_6=22,b_6=1,c_6=3,d_6=9 \\ {a}_7=24,b_7=0,c_7=3,d_7=9 \\ d=0{\dots }_3 \end{gathered}$$

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