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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Step 1: Solve the linear equation for x. 2x - 1 = 11 Add 1 to both sides: 2x = 11 + 1 2x = 12 Divide by 2: x = (12)/(2) x = 6 The value of x is 6. Step 2: Convert ₵45.62 to pesewas. Assuming "bo" is a typo for "pesewas" and ₵1 = 100 pesewas. 45.62 Cedi × 100 pesewasCedi = 4562 pesewas ₵45.62 is equal to 4562 pesewas. Step 3: Calculate the amount paid after a discount. Original cost = ₵200 Discount = 30% Discount amount = 30\% of ₵200 0.30 × 200 = 60 Discount amount = ₵60 Amount paid = Original cost - Discount amount 200 - 60 = 140 The buyer will pay ₵140. Step 4: Solve for x. Assuming the equation is 2 × x × 9 = 648. 18x = 648 Divide by 18: x = (648)/(18) x = 36 The value of x is 36. Step 5: Calculate the perimeter of the rectangular field. Length (L) = 100 m Breadth (W) = 50 m Perimeter (P) = 2(L + W) P = 2(100 m + 50 m) P = 2(150 m) P = 300 m The perimeter of the rectangular field is 300 m. Step 6: Calculate the perimeter of the rhombus. A rhombus has four equal sides. Assuming the side length is 5 cm (taking the first value given, as "5cm by 8cm" is contradictory for a rhombus). Side length (s) = 5 cm Perimeter (P) = 4s P = 4 × 5 cm P = 20 cm The perimeter of the rhombus is 20 cm. Step 7: Find the cost price. Selling Price (SP) = ₵14 Profit = 40% Let Cost Price (CP) be x. SP = CP + Profit SP = CP + (Profit % of CP) 14 = x + 0.40x 14 = 1.40x Divide by 1.40: x = (14)/(1.40) x = 10 The cost price is ₵10. Step 8: Simplify the ratio. Ratio = 18:45 Find the greatest common divisor (GCD) of 18 and 45. Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 45: 1, 3, 5, 9, 15, 45 The GCD is 9. Divide both parts of the ratio by 9: (18)/(9) : (45)/(9) 2 : 5 The ratio in its lowest term is 2:5. Step 9: Calculate C's share. Total amount = ₵48 Ratio A:B:C = 2:3:5 Total ratio parts = 2 + 3 + 5 = 10 C's share = C's ratio partTotal ratio parts × Total amount C's share = (5)/(10) × 48 C's share = (1)/(2) × 48 C's share = 24 C's share is ₵24. Step 10: Calculate the number of years. Principal (P) = ₵800 Amount (A) = ₵960 Interest (I) = A - P = ₵960 - ₵800 = ₵160 Interest Rate (R) = 5% per annum = 0.05 Simple Interest formula: I = P × R × T 160 = 800 × 0.05 × T 160 = 40 × T Divide by 40: T = (160)/(40) T = 4 The money was in the bank for 4 years. Step 11: Convert Cedi to Pounds. Assuming the conversion rate is £1 = ₵300. Amount in Cedi = ₵27,000 Amount in Pounds = Amount in CediCedi per Pound Amount in Pounds = (27000)/(300) Amount in Pounds = 90 You could get £90. Step 12: Find the profit or loss. Cost Price (CP) = ₵75 Selling Price (SP) = ₵63 Since SP < CP, there is a loss. Loss = CP - SP 75 - 63 = 12 The loss is ₵12.