Let's start from the definition of average:
\(\displaystyle (\text{Average}) = \frac{(\text{Total # of points})}{(\text{# of reviews})}\)
Plugging in the known information gives us:
\(\displaystyle 3.6 = \frac{(\text{Total # of points})}{x}\)
\(\displaystyle (\text{Total # of points}) = 3.6x\)
That re-establishes what Subhotosh Khan's hint told you, but now what would we do? Well, we can use the exact same principle to derive when the average will be 4.6 points. Since we don't know how many new reviews we need, let's give that variable a name so we can talk about it. Call it \(k\). Setting up the definition of average again:
\(\displaystyle 4.6 = \frac{3.6x + ???}{x + k}\)
We know that each new review is guaranteed to be a 5-star review, so how many new points would \(k\) 5-star reviews add to the total? How does having this complete fraction help you solve for \(k\)? Note that your answer will not be a numerical one, but rather you'll find that \(k\) is a function of \(x\).
