To find the average weight of the pies, we first need to calculate the total weight of all the pies and then divide that by the number of pies (which is 8).
Let's calculate the total weight step by step:
-
Two pies weigh 105 g each:
\( 2 \times 105 = 210 , \text{g} \) -
One pie weighs 106 g:
\( 106 , \text{g} \) -
Two pies weigh 108 g each:
\( 2 \times 108 = 216 , \text{g} \) -
One pie weighs 103.5 g:
\( 103.5 , \text{g} \) -
One pie weighs 102 g:
\( 102 , \text{g} \) -
One pie weighs 104.5 g:
\( 104.5 , \text{g} \)
Now, let's add all these weights together:
\[ \text{Total weight} = 210 , \text{g} + 106 , \text{g} + 216 , \text{g} + 103.5 , \text{g} + 102 , \text{g} + 104.5 , \text{g} \]
Calculating it step by step:
- \( 210 + 106 = 316 \)
- \( 316 + 216 = 532 \)
- \( 532 + 103.5 = 635.5 \)
- \( 635.5 + 102 = 737.5 \)
- \( 737.5 + 104.5 = 842 \)
So, the total weight of the pies is 842 g.
Next, we'll calculate the average weight by dividing the total weight by the number of pies:
\[ \text{Average weight} = \frac{\text{Total weight}}{\text{Number of pies}} = \frac{842 , \text{g}}{8} \]
Doing the division:
\[ \frac{842}{8} = 105.25 , \text{g} \]
Thus, the average weight of the pies, rounded to two decimal places, is:
\[ \boxed{105.25} \]