The weight of each bag filled by Brandon, is [tex]\fbox{\bf1.675\,lb}[/tex].
Further explanation:
The amount of cashews and pistachios mixed are [tex]6.83\,lb[/tex] and [tex]3.57\,lb[/tex] respectively then the total weight of mixture is the sum of cashews and pistachios.
After the above nut mixture created by mixing cashews and pistachios is filled in six bags, the weight of remaining nuts is [tex]0.35\,lb[/tex].
Therefore, the total mixture that is filled in 6 bags is obtained as the difference of total amount and the remaining mixture amount.
[tex]\begin{aligned}{\text{Total mixture filled in six bags}}&=6.83+3.57-0.35\\&=10.4-0.35\\&=10.05\\\end{aligned}[/tex]
Now, this obtained amount of mixture weighing [tex]10.05\,lb[/tex] is filled equally in 6 bags as the size of bags is same then the amount of mixture in one bag or each bag is calculated as,
[tex]\begin{aligned}{\text{Total mixture filled in each bags}}&=\frac{{10.05}}{6}\\&=1.675\\\end{aligned}[/tex]
Thus, the weight of each of the six bags that Brandon fills, is [tex]\fbox{\bf1.675\,lb}[/tex].
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Mixtures and ratios
Keywords: cashews, pistachios, one bag, six bag, each bag, weight, Brandon, same size, mixture, nuts, 6.83lb, 3.57lb, 0.35lb, total mixture, amount of mixture, remaining amount, remaining weight, total weight, nut mixture.
