A motel is owned by three people. Mrs.X owns 3/5 of the Motel, and Mr.Y owns twice as much as Mr.Z. What fraction of the motel does Mr.Z own?
To find out what fraction of the motel Mr.Z owns, we first need to determine the ownership fraction of Mr.Y and then use that information to find Mr.Z's ownership fraction.
We are given that Mrs.X owns 3/5 of the motel. Since there are three owners in total, we can subtract Mrs.X's ownership fraction from 1 to find the combined ownership fraction of Mr.Y and Mr.Z.
1 - 3/5 = 5/5 - 3/5 = 2/5
Now, we know that Mr.Y owns twice as much as Mr.Z, which means that the ownership fraction of Mr.Y is twice that of Mr.Z.
Let's call the ownership fraction of Mr.Z as "z." Therefore, the ownership fraction of Mr.Y is 2z.
To find the combined ownership fraction of Mr.Y and Mr.Z, we can add their ownership fractions:
2z + z = 3z
We know that the combined ownership fraction of Mr.Y and Mr.Z is 2/5, so we can set up the following equation:
3z = 2/5
To find the value of z, we can solve the equation:
z = (2/5) / 3 = 2/5 * 1/3 = 2/15
Hence, Mr.Z owns 2/15 of the motel.