This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Morning black — let's get this done. Here are the solutions for questions 44, 45, 46, and 47. Question 44: Step 1: Calculate the sales amount on which commission is paid. Commission is paid on sales above KSh 50,000. Sales for commission = Total sales - Threshold Sales for commission = KSh 350,000 - KSh 50,000 = KSh 300,000 Step 2: Calculate the commission earned. Commission rate is 15%. Commission = 15\% × KSh 300,000 Commission = (15)/(100) × 300,000 = 15 × 3,000 = KSh 45,000 Step 3: Calculate Mary's total earnings for the month. Total earnings = Fixed monthly salary + Commission Total earnings = KSh 30,000 + KSh 45,000 = KSh 75,000 Mary earned KSh 75,000 that month. Your calculation for Question 44 is ❌ Incorrect. The commission should be calculated only on the amount above KSh 50,000, not on the total sales. Question 45: Let Jane's age be j. Peter is twice as old as Jane, so Peter's age is 2j. a) Write an expression for the sum of their ages. Sum of ages = Jane's age + Peter's age Sum of ages = j + 2j = 3j The expression for the sum of their ages is 3j. b) Work out the sum of their ages if Jane's age is 12 years. Substitute j = 12 into the expression from part (a). Sum of ages = 3 × 12 = 36 years The sum of their ages is 36 years. Your work for Question 45 is ✅ Correct. Question 46: Based on the diagram provided: The given