Let us take the case of 7 pounds for $8.47 first.
7 pounds of a product costs = 8.47 dollars
Then
1 pound of the same product will cost = (8.47/7) dollars
= 1.21 dollars
Now let us take the case of 9 pounds for $11.07
9 pounds of a product costs = 11.07 dollars
Then
1 pound of the same product will cost = (11.07/9) pounds
= 1.23 dollars
So from the above deductions we can see that 9 pounds for $11.07 is a better buy than 7 pounds for $8.47. I hope the procedure is clear enough for you to understand. In future you can use this method for solving similar problems.
Using the given equation, take the square root of both sides. Both 169 and 9 are perfect squares, so the left side becomes plus or minus 13/3, which is rational. Six plus 13/3 is a rational number, and 6 minus 13/3 is also a rational number. If the solutions of a quadratic equation are rational, then the equation is factorable.