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Ten years ago, Brian was twice as old as...

Ten years ago, Brian was twice as old as Aubrey.
`{:("Quantity A","Quantity B"),("Twice Aubrey's age today","Brian's age today"):}`

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To solve the problem step by step, let's define the ages of Brian and Aubrey based on the information provided. ### Step 1: Define Variables Let: - \( A \) = Aubrey's current age - \( B \) = Brian's current age ### Step 2: Set Up the Equation from the Given Information According to the problem, ten years ago, Brian was twice as old as Aubrey. This can be expressed as: - Ten years ago, Aubrey's age = \( A - 10 \) - Ten years ago, Brian's age = \( B - 10 \) From the information given: \[ B - 10 = 2(A - 10) \] ### Step 3: Simplify the Equation Now, let's simplify the equation: \[ B - 10 = 2A - 20 \] Adding 10 to both sides gives: \[ B = 2A - 10 \] ### Step 4: Express the Quantities to Compare Now we need to express the two quantities we are comparing: - **Quantity A**: Twice Aubrey's age today \[ \text{Quantity A} = 2A \] - **Quantity B**: Brian's age today \[ \text{Quantity B} = B = 2A - 10 \] ### Step 5: Compare the Two Quantities Now we need to compare \( 2A \) and \( 2A - 10 \): \[ 2A \quad \text{vs} \quad 2A - 10 \] ### Step 6: Determine the Relationship To compare these, we can subtract \( 2A - 10 \) from \( 2A \): \[ 2A - (2A - 10) = 10 \] Since \( 10 > 0 \), we conclude that: \[ 2A > 2A - 10 \] Thus, **Quantity A** is greater than **Quantity B**. ### Final Conclusion Therefore, we can conclude that: \[ \text{Quantity A} > \text{Quantity B} \] ---
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