Step 1 :Let the total number of bags sold be represented by \(total\_bags = 5670\)
Step 2 :Let the number of fat free bags sold be represented by \(fat\_free\_bags = 5120\)
Step 3 :To find the percentage of bags that were fat free, we need to divide the number of fat free bags by the total number of bags sold, and then multiply the result by 100. This can be represented by the formula \(percentage = \frac{fat\_free\_bags}{total\_bags} \times 100\)
Step 4 :Substituting the given values into the formula, we get \(percentage = \frac{5120}{5670} \times 100 = 90.29982363315696\)
Step 5 :Rounding this to the nearest percent, we get \(rounded\_percentage = 90\)
Step 6 :Final Answer: The percentage of bags that were fat free is \(\boxed{90\%}\)