Answer :
Let's go through the problem step-by-step:
1. The employee works 35 hours per week.
2. The aim is to find an inequality representing the condition for earning more than [tex]$400 per week. 3. We assume the hourly wage of the employee is $[/tex]8.
Firstly, the income from hourly wages can be calculated:
[tex]\[ 35 \text{ hours/week} \times 8 \text{ dollars/hour} = 280 \text{ dollars/week} \][/tex]
Next, we need to account for the weekly sales, represented by [tex]\( x \)[/tex]. The employee earns an additional 8% commission on these sales:
[tex]\[ 0.08x \][/tex]
So, the total weekly earnings, including both the hourly wage and sales commission, is:
[tex]\[ 280 + 0.08x \][/tex]
To find the weekly sales [tex]\( x \)[/tex] required to earn more than [tex]$400 per week, we set up the following inequality: \[ 280 + 0.08x > 400 \] Now, we break it down further: Subtract 280 from both sides to isolate the term with \( x \): \[ 280 + 0.08x - 280 > 400 - 280 \] \[ 0.08x > 120 \] The simplified inequality is: \[ x > 1500 \] Thus, the inequality that represents the condition for the employee to earn more than $[/tex]400 per week is:
[tex]\[ 35(8) + 0.08x > 400 \][/tex]
So, option B is correct:
[tex]\[ 35(8)+0.08 x>400 \][/tex]
1. The employee works 35 hours per week.
2. The aim is to find an inequality representing the condition for earning more than [tex]$400 per week. 3. We assume the hourly wage of the employee is $[/tex]8.
Firstly, the income from hourly wages can be calculated:
[tex]\[ 35 \text{ hours/week} \times 8 \text{ dollars/hour} = 280 \text{ dollars/week} \][/tex]
Next, we need to account for the weekly sales, represented by [tex]\( x \)[/tex]. The employee earns an additional 8% commission on these sales:
[tex]\[ 0.08x \][/tex]
So, the total weekly earnings, including both the hourly wage and sales commission, is:
[tex]\[ 280 + 0.08x \][/tex]
To find the weekly sales [tex]\( x \)[/tex] required to earn more than [tex]$400 per week, we set up the following inequality: \[ 280 + 0.08x > 400 \] Now, we break it down further: Subtract 280 from both sides to isolate the term with \( x \): \[ 280 + 0.08x - 280 > 400 - 280 \] \[ 0.08x > 120 \] The simplified inequality is: \[ x > 1500 \] Thus, the inequality that represents the condition for the employee to earn more than $[/tex]400 per week is:
[tex]\[ 35(8) + 0.08x > 400 \][/tex]
So, option B is correct:
[tex]\[ 35(8)+0.08 x>400 \][/tex]
