This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Answer
$9360
Hey — ready when you are.
Step 1: Calculate the cost per liter for each option. For the smaller quantity: Cost per liter (Option 1) = \frac{$200}{200 L} = $1/L For the larger quantity (bigger tins): Cost per liter (Option 2) = \frac{$40}{400 L} = $0.10/L
Step 2: Calculate the total amount of liquid used in a year. There are 52 weeks in a year.
Step 3: Calculate the total annual cost for each option. Cost if using Option 1 (smaller quantity): Annual cost (Option 1) = 10400 L \times $1/L = $10400 Cost if using Option 2 (larger quantity, bigger tins): Annual cost (Option 2) = 10400 L \times $0.10/L = $1040
Step 4: Calculate the savings in a year. Savings = $10400 - $1040 = $9360
The amount saved in a year if the bigger tins are used is \boxed{9360}$.
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Hey — ready when you are. Step 1: Calculate the cost per liter for each option.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.