First, you need to remember that, in math, a Ratio is used to compare two values.
By definition, a ratio can be written as a fraction, as following:
[tex]\frac{a}{b}[/tex]Where "a" is the numerator and "b" is the denominator. This ratio is read as "a to b".
In this case you know that after buy some bikes, Lois owns 174 bikes, and before that she owned 29. Then, you can calculate the number of bikes purchased as following:
[tex]174-29=145[/tex]Then you can set up that:
[tex]\begin{gathered} a=145 \\ b=174 \end{gathered}[/tex]Therefore, the ratio of bikes purchased to resulting total number of bikes is:
[tex]=\frac{145}{174}=\frac{5}{6}[/tex]The answer is:
[tex]\frac{5}{6}[/tex]