Here are the answers for the given problems:

Review Exercises

Compute the straight commission:

44. $7,600 \times 0.04 = 304$

45. $122,360 \times 0.0625 = 7,647.50$

Compute the straight commission and gross pay:

46. $3,790 \times 0.065 = 246.35$

• Compare to minimum salary of $185.
• Gross pay = $246.35 (since it is higher)

47. $1,515 \times 0.0565 = 85.60$

• Compare to minimum salary of $250.
• Gross pay = $250 (since it's higher)

48. $98,000 \times 0.07 = 6,860$

49. $26,348 \times 0.18 = 4,742.64$

50. $4,190 - 1,950 = 2,240$
    $\frac{2,240}{0.0675} \approx 33,185.19$

• Total sales = $33,185.19

Graduated Commission

Compute the total graduated commission:

• $1,900 \times 0.25 = 475$
• $(3,500 - 1,900) \times 0.27 = 432$
• Total commission = 475 + 432 = 907

• $4,000 \times 0.05 = 200$
• $6,000 \times 0.06 = 360$
• $(12,360 - 10,000) \times 0.11 = 259.60$
• Total commission = 200 + 360 + 259.60 = 819.60

• $5,000 \times 0.05 = 250$
• $15,000 \times 0.065 = 975$
• $(23,458 - 20,000) \times 0.07 = 242.06$
• Total commission = 250 + 975 + 242.06 = 1,467.06

• $10 \times 5 = 50$
• $2 \times 6 = 12$
• $4 \times 10.55 = 42.20$
• Total commission = 50 + 12 + 42.20 = 104.20

• Let $x$ be the total sales.
• For $x \leq 5,000$, commission $= 0.07x$.
• For $x > 5,000$, commission $= 0.07 \times 5,000 + 0.09(x - 5,000)$.
• Given gross pay of $578, solve for $x$:
  $0.07 \times 5,000 + 0.09(x - 5,000) = 578$
  $350 + 0.09(x - 5,000) = 578$
  $0.09(x - 5,000) = 228$
  $x - 5,000 = 2,533.33$
  $x = 7,533.33$
• Total sales = $7,533.33

Would you like further explanations or details on any of these calculations?

Here are 5 questions that expand on these concepts:

1. What factors determine whether the gross pay is the minimum salary or the commission in sales?
2. How do you calculate commissions when multiple rates apply over different sales levels?
3. What is the importance of comparing the straight commission to the guaranteed minimum salary in certain jobs?
4. How would increasing the commission rate affect the gross pay in each problem?
5. What would happen to the sales commission if the total sales had a different distribution?

Tip: For commissions, always break down the sales into their respective ranges and apply the correct rate before summing up the total.