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Sagot :
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].
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].
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