The Tourists Are Accommodated In 3 Hotels. There Are 8 More Tourists In The Second Hotel Than In The First Hotel And In The Third Hotel There Are 14 M

The tourists are accommodated in 3 hotels. There are 8 more tourists in the second hotel than in the first hotel and in the third hotel there are 14 more tourists than in the second hotel. If there is a total of 258 tourists, how many tourists are accommodated in each of the hotels? please show solution. Thanks!

 

Answer:

\left\begin{array}{ccc}First\:hotel:&76\:tourists\\Second\:hotel:&84\:tourists\\Third\:hotel:&98\:tourists\end{array}\right

Computation:

Representation

Number\:of\:tourists\\\\\left\begin{array}{ccc}First\:hotel&\to&x\\Second\:hotel&\to&x+8\\Third\:hotel&\to&x+8+14\end{array}\right

Solving for the number of tourists in each hotel.

First\:hotel:\\x+x+8+x+8+14=258\\3x+30=258\\3x=258-30\\3x=228\\x=228/3=76\\\\Second\:hotel:\\x+8=76+8=84\\\\Third\:hotel:\\x+8+14=76+8+14=98

Check

76+84+98=258\\160+98=258\\258=258\:\:\:\checkmark


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