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7. Reason Abstractly The number of customers in a store on the first day is represented by \( (6 x-3) \). The number of customers on the second day is represented by \( (x-1) \). Write an expression to find how many more customers visited the store on the first day. Then evaluate the expression if \( x \) is equal to 50 . (Example 6 )

Ask by Elliott Kelley. in the United States
Feb 03,2025

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Answer

The expression to find how many more customers visited on the first day is \(5x - 2\). When \(x = 50\), 248 more customers visited on the first day.

Solution

To determine how many more customers visited the store on the **first day** compared to the **second day**, follow these steps: 1. **Identify the Expressions:** - **First Day Customers:** \( 6x - 3 \) - **Second Day Customers:** \( x - 1 \) 2. **Set Up the Expression for the Difference:** To find how many more customers visited on the first day, subtract the number of customers on the second day from the number on the first day. \[ \text{Difference} = (6x - 3) - (x - 1) \] 3. **Simplify the Expression:** \[ \begin{align*} \text{Difference} &= 6x - 3 - x + 1 \\ &= (6x - x) + (-3 + 1) \\ &= 5x - 2 \end{align*} \] So, the expression to find how many more customers visited on the first day is: \[ 5x - 2 \] 4. **Evaluate the Expression When \( x = 50 \):** Substitute \( x = 50 \) into the expression: \[ \begin{align*} \text{Difference} &= 5(50) - 2 \\ &= 250 - 2 \\ &= 248 \end{align*} \] **Therefore,** when \( x = 50 \), **248 more customers** visited the store on the first day compared to the second day.

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To find how many more customers visited the store on the first day than the second day, you'll subtract the expression for the second day from the expression for the first day. So the expression will be: \[ (6x - 3) - (x - 1) \] This simplifies to \( 6x - 3 - x + 1 = 5x - 2 \). Now, if you evaluate this expression for \( x = 50 \): \[ 5(50) - 2 = 250 - 2 = 248 \]. Thus, 248 more customers visited the store on the first day than the second day. Isn’t it fascinating how we can analyze customer trends with simple algebra? This type of abstract reasoning can help businesses strategize. When solving similar problems, remember to carefully distribute negative signs when subtracting expressions; it’s a common mistake that can lead to incorrect answers and confusion!

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