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A) Which of the following is not true?

1. A line with the equation [tex]x + y = 7[/tex].

2. A sine that is parallel to the x-axis. The slope of a line parallel to the x-axis is 0.

3. A line with an undefined slope, meaning it is vertical.

4. The larger the slope, the steeper the line relative to the vertical axis.

B) A salesman has a basic weekly salary of $200. In addition, he receives a sales commission of 20% of his total volume of sales. State the relationship between his weekly salary [tex]Y[/tex] and his sales [tex]X[/tex].

A. [tex]Y = 20X + 200[/tex]
B. [tex]Y = 0.20X + 200[/tex]
C. [tex]Y = 200X + 20[/tex]
D. None of the above



Answer :

GinnyAnswer
Sure, let’s work through the problem step by step.

Problem Statement:
A salesman has a basic weekly salary of $200 and is entitled to a commission of 20% on his total sales volume. The question provides options for the equation representing his total weekly earnings \( Y \) based on his sales \( X \):

A) \( Y = 20X + 200 \)
B) \( Y = 0.20X + 200 \)
C) \( Y = 200X + 20 \)
D) None of the above

Given Parameters:
- Basic weekly salary = \( \$200 \)
- Commission rate = \( 20\% \) or \( 0.20 \)
- Weekly sales (let's denote it as \( X \))

Let's break down the information and find the correct equation step by step:

1. Calculate Weekly Earnings:
The formula for total weekly earnings \( Y \) can be obtained by adding the basic salary and the sales commission.

[tex]\[ Y = \text{Basic salary} + (\text{Commission rate} \times \text{Sales}) \][/tex]

Substituting the given parameters:

[tex]\[ Y = 200 + (0.20 \times X) \][/tex]

2. Verify Each Given Equation:
Let's evaluate the given equations:

- Option A: \( Y = 20X + 200 \)
Substituting weekly sales \( X = 200 \):

[tex]\[ Y_A = 20(200) + 200 = 4000 + 200 = 4200 \][/tex]

- Option B: \( Y = 0.20X + 200 \)
Substituting weekly sales \( X = 200 \):

[tex]\[ Y_B = 0.20(200) + 200 = 40 + 200 = 240 \][/tex]

- Option C: \( Y = 200X + 20 \)
Substituting weekly sales \( X = 200 \):

[tex]\[ Y_C = 200(200) + 20 = 40000 + 20 = 40020 \][/tex]

- Option D: None of these (considered if none of the above are correct)

3. Compare the Results:
- The calculated total weekly earnings should be based on the correct relationship:

Based on the \$200 basic salary and 20\% commission on sales
[tex]\[ Y = 200 + 0.20X \][/tex]

- Verify the numerical results for \( X = 200 \):
- \( Y_A = 4200 \) does not match the correct result.
- \( Y_B = 240 \) is the correct result.
- \( Y_C = 40020 \) does not match the correct result.

Conclusion:
From the calculations, option B (\( Y = 0.20X + 200 \)) correctly represents the total weekly earnings of the salesman based on the given salary and commission structure.

Thus, the correct equation is Option B: [tex]\( Y = 0.20X + 200 \)[/tex].