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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Here are the solutions to your questions: 14. A bicycle has a cash price of Ksh 18,000. Peter buys it on hire purchase by paying a deposit of Ksh 4,000 and 10 monthly installments of Ksh 1,600 each. How much more did he pay for the bicycle on hire purchase than its cash price? Step 1: Calculate the total cost of the bicycle on hire purchase. The deposit is Ksh 4,000. The total amount paid in installments is the number of installments multiplied by the amount per installment. Total installments = 10 × Ksh 1,600 = Ksh 16,000 The total hire purchase cost is the sum of the deposit and the total installments. Total hire purchase cost = Ksh 4,000 + Ksh 16,000 = Ksh 20,000 Step 2: Calculate the difference between the hire purchase cost and the cash price. The cash price is Ksh 18,000. Difference = Total hire purchase cost - Cash price Difference = Ksh 20,000 - Ksh 18,000 = Ksh 2,000 Peter paid Ksh 2,000 more for the bicycle on hire purchase. Ksh 2,000 15. Peter is twice as old as his sister, Jane. Let Jane's age be j. a) Write an expression for the sum of their ages. Peter's age is twice Jane's age, so Peter's age is 2j. The sum of their ages is Jane's age plus 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 The sum of their ages is 36 years. 36 years 16. On the graph grid provided below plot the following points: A (-2,4), B (0,0), C (1,-1), C (3,1) and join (3mks) Assuming the second 'C' is meant to be a distinct point, let's call it D (3,1). Step 1: Plot point A (-2,4). Start at the origin (0,0). Move 2 units to the left along the x-axis, then 4 units up along the y-axis. Mark this point as A. Step 2: Plot point B (0,0). This is the origin. Mark this point as B. Step 3: Plot point C (1,-1). Start at the origin (0,0). Move 1 unit to the right along the x-axis, then 1 unit down along the y-axis. Mark this point as C. Step 4: Plot point D (3,1). Start at the origin (0,0). Move 3 units to the right along the x-axis, then 1 unit up along the y-axis. Mark this point as D. Step 5: Join the points. Draw a straight line segment from A to B. Draw a straight line segment from B to C. Draw a straight line segment from C to D. Last free one today — make it count tomorrow, or type /upgrade for unlimited.