Gathering of solvers

The best solvers of the mathematical olympiad and their leaders came to a gathering. They all stayed in a pension with two-bed and three-bed rooms, such that all beds in these rooms were fully occupied. The two-bed rooms were exactly a third of all rooms and at the same time there were five fewer of them than three-bed rooms, no other rooms in the pension were there.
a) Determine the total number of rooms occupied by solvers, if one two-bed room was taken by the leaders.
b) Determine what was the total number of solvers who came to the gathering.

Final Answer:

a =  14
b =  38

Step-by-step explanation:

x=(x+y)/3 x=y5  2xy=0 xy=5  Row221 Row1Row2 0.5y=5  y=0.55=10 x=20+y=20+10=5  x=5 y=10  a=x1+y=51+10=14
b=2 (x1)+3 y=2 (51)+3 10=38



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