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Eric earns a weekly salary and a commission on each item that he sells. The equation [tex]y = 10x + 50[/tex] represents the amount of money that Eric earns weekly. Bailey earns a greater weekly salary than Eric but the same commission rate.

Which graph could represent the amount of money that Bailey earns weekly, [tex]y[/tex], based on the number of items sold, [tex]x[/tex]?

Sagot :

GinnyAnswer
To determine the equation that represents the amount of money Bailey earns weekly given that she earns a greater weekly salary than Eric but has the same commission rate, let's break it down step-by-step.

### Step-by-Step Solution:

1. Understanding Eric's Earnings:
- Eric's weekly earnings are given by the equation [tex]\(y = 10x + 50\)[/tex].
- In this equation:
- [tex]\( y \)[/tex] is the total weekly earnings.
- [tex]\( x \)[/tex] is the number of items sold.
- The coefficient [tex]\( 10 \)[/tex] represents a commission rate of [tex]$10 per item sold. - The constant term \( 50 \) represents Eric's fixed weekly salary. 2. Identifying Bailey's Weekly Earnings: - Bailey has the same commission rate of $[/tex]10 per item sold.
- However, it is stated that her weekly salary is greater than Eric's, which means the constant term in her earnings equation will be greater than [tex]$50. 3. Formulating Bailey's Earnings: - Since the commission per item remains the same, the coefficient for \( x \) in Bailey's earnings equation will also be \( 10 \). - The crucial difference lies in her fixed weekly salary, which must be greater than $[/tex]50. We need to represent this greater weekly salary using different values.
- We will consider different possible higher weekly salaries to represent Bailey's earnings. Let’s choose [tex]\( 60 \)[/tex], [tex]\( 70 \)[/tex], and [tex]\( 80 \)[/tex] as sample higher weekly salaries for illustration.

4. Resulting Equations for Bailey's Earnings:
- For a weekly salary of [tex]$60, Bailey's earnings can be represented by the equation \( y = 10x + 60 \). - For a weekly salary of $[/tex]70, Bailey's earnings can be represented by the equation [tex]\( y = 10x + 70 \)[/tex].
- For a weekly salary of $80, Bailey's earnings can be represented by the equation [tex]\( y = 10x + 80 \)[/tex].

### Conclusion:

Bailey's weekly earnings, based on the number of items sold, can be represented by any of the following equations, depending on her specific salary:
1. [tex]\( y = 10x + 60 \)[/tex]
2. [tex]\( y = 10x + 70 \)[/tex]
3. [tex]\( y = 10x + 80 \)[/tex]

These equations illustrate that for [tex]\( x \)[/tex] items sold, the amount of money Bailey earns weekly will be more than Eric’s because her weekly salary (represented by the constant term) is greater.
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