To calculate the grand total Jesse will be paying, we need to consider the cost of the food, the sales tax, and the tip.
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Calculate the sales tax: The sales tax is 9% of the food cost. \[ \text{Sales Tax} = \text{Food Cost} \times \text{Sales Tax Rate} = 105.79 \times 0.09 \] \[ \text{Sales Tax} = 9.4711 \]
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Calculate the total cost including sales tax: \[ \text{Total Cost with Tax} = \text{Food Cost} + \text{Sales Tax} = 105.79 + 9.4711 \] \[ \text{Total Cost with Tax} = 115.2611 \]
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Calculate the tip: The tip is 40% of the total cost with tax. \[ \text{Tip} = \text{Total Cost with Tax} \times \text{Tip Rate} = 115.2611 \times 0.40 \] \[ \text{Tip} = 46.10444 \]
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Calculate the grand total: \[ \text{Grand Total} = \text{Total Cost with Tax} + \text{Tip} = 115.2611 + 46.10444 \] \[ \text{Grand Total} = 161.36554 \]
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Round to the nearest hundredth: \[ \text{Grand Total (rounded)} = 161.37 \]
Thus, Jesse's grand total for lunch is $161.37.