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.
ScanSolve AI Answer
a) Step 1: Calculate the loss amount. Loss is 5% of M40 000. Loss = 0.05 × 40000 = M2000 Step 2: Calculate the selling price. Selling price is the original price minus the loss. Selling Price = 40000 - 2000 = M38000 The selling price is M38000. b) Step 1: Use the compound interest formula to find the value after three years. The formula for compound interest is A = P(1 + r)^n, where A is the final amount, P is the principal amount, r is the annual interest rate, and n is the number of years. Given P = M50000, r = 4\% = 0.04, and n = 3 years. A = 50000(1 + 0.04)^3 Step 2: Calculate the final value. A = 50000(1.04)^3 A = 50000 × 1.124864 A = M56243.20 The price of the land after three years is M56243.20. c) (i) Step 1: Calculate the amount by which the large milkshake is bigger. The large milkshake is (2)/(3) more than the small milkshake. Increase = (2)/(3) × 300 ml = 200 ml Step 2: Find the size of the large milkshake. Large milkshake = Small milkshake + Increase Large milkshake = 300 ml + 200 ml = 500 ml The size of the large milkshake is 500 ml. (ii) Step 1: Express the ratio of the small milkshake to the large milkshake. Small milkshake : Large milkshake = 300 ml : 500 ml Step 2: Simplify the ratio. Divide both sides by 100. 300 : 500 = 3 : 5 The ratio in its simplest form is 3:5. d) Step 1: Calculate the total simple interest earned. The formula for simple interest is I = A - P, where I is the interest, A is the final amount, and P is the principal. Given A = M17400 and P = M12000. I = 17400 - 12000 = M5400 Step 2: Use the simple interest formula to find the rate r. The formula for simple interest is I = (PRT)/(100), where P is the principal, R is the rate, and T is the time in years. Given I = M5400, P = M12000, and T = 3 years. 5400 = (12000 × r × 3)/(100) Step 3: Solve for r. 5400 = 120 × r × 3 5400 = 360r r = (5400)/(360) r = 15 The value of r is 15. Drop the next question.