The first game has the chance of winning is 1, the chance of losing is 5.(not fair)

The second game has the chance of winning is 2, the chance of losing is 4.(not fair)

The third game has the chance of winning is 2, the chance of losing is 4.(not fair)

The fourth game has the chance of winning is 2, the chance of losing is 4.(not fair)

The fifth game has the chance of winning is 3, the chance of losing is 3.(fair)

So the (E) game is fair.

From \(\dfrac{5a+7b}{6a+5b}=\dfrac{29}{28}\)we have:

\(29\left(6a+5b\right)=28\left(5a+7b\right)\)

\(\Rightarrow174a+145b=140a+196b\)

\(\Rightarrow34a=51b\)

\(\Rightarrow2a=3b\)

\(\Rightarrow\dfrac{a}{b}=\dfrac{3}{2}\)

\(\Rightarrow a=3k;b=2k\)

Because GCM(a,b)=1 so k=1. That means a=3, b=2.

We have this equation\(\left\{{}\begin{matrix}a=3b\\a-3=b+3\end{matrix}\right.\)(with a is the length and b is the width)

\(\Rightarrow3b-3=b+3\)

\(\Rightarrow3b=b+6\)

\(\Rightarrow2b=6\)

\(\Rightarrow b=3\)

\(\Rightarrow a=9\)

So that the rug is 3m wide and 9m long.

does she buy / buys