First, we need to calculate the total weight of the mixture which consists of raisins and almonds.
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Convert the mixed weights into improper fractions:
- Raisins: \( 3 \frac{5}{8} = 3 + \frac{5}{8} = \frac{24}{8} + \frac{5}{8} = \frac{29}{8} \) pounds
- Almonds: \( 4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} = \frac{36}{8} \) pounds
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Now add the two weights together:
\[ \text{Total weight} = \text{Weight of raisins} + \text{Weight of almonds} = \frac{29}{8} + \frac{36}{8} = \frac{29 + 36}{8} = \frac{65}{8} \text{ pounds} \]
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Next, we need to determine how many bags of \( \frac{5}{8} \) pounds each can be made from the total mixture. To find this, divide the total weight of the mixture by the weight of each bag:
\[ \text{Number of bags} = \frac{\text{Total weight}}{\text{Weight per bag}} = \frac{\frac{65}{8}}{\frac{5}{8}} \]
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When dividing fractions, multiply by the reciprocal:
\[ \frac{\frac{65}{8}}{\frac{5}{8}} = \frac{65}{8} \times \frac{8}{5} = \frac{65 \times 8}{8 \times 5} = \frac{65}{5} = 13 \]
So, Ken makes 13 bags of the mixture.