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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Right Mohaa, let's go. a) Step 1: Calculate the total cost of Wairimu beans. Cost of Wairimu = 30 bags × Ksh. 4000/bag = Ksh. 120,000 Step 2: Calculate the total cost of Yellow Green beans. Cost of Yellow Green = 50 bags × Ksh. 3500/bag = Ksh. 175,000 Step 3: Calculate the total cost of the mixture. Total cost = Ksh. 120,000 + Ksh. 175,000 = Ksh. 295,000 Step 4: Calculate the total number of bags in the mixture. Total bags = 30 + 50 = 80 bags Step 5: Calculate the cost price per bag of the mixture. Cost price per bag = Ksh. 295,00080 bags = Ksh. 3687.50/bag Step 6: Calculate the selling price per bag with a 20% profit. Selling price per bag = Cost price per bag × (1 + Profit percentage) Selling price per bag = Ksh. 3687.50 × (1 + 0.20) Selling price per bag = Ksh. 3687.50 × 1.20 = Ksh. 4425 The selling price of one bag of the mixture is Ksh. 4425. b) Let a be the number of bags of Wairimu and b be the number of bags of Yellow Green. The cost of Wairimu is Ksh. 4,000 per bag. The cost of Yellow Green is Ksh. 3,500 per bag. The cost of the mixture is Ksh. 3,835 per bag. Step 1: Set up the equation for the weighted average cost. (a × 4000 + b × 3500)/(a+b) = 3835 Step 2: Multiply both sides by (a+b). 4000a + 3500b = 3835(a+b) 4000a + 3500b = 3835a + 3835b Step 3: Group terms with a and terms with b. 4000a - 3835a = 3835b - 3500b 165a = 335b Step 4: Find the ratio a:b. (a)/(b) = (335)/(165) Step 5: Simplify the ratio by dividing the numerator and denominator by their greatest common divisor, which is 5. (a)/(b) = (335 ÷ 5)/(165 ÷ 5) = (67)/(33) The ratio a:b is 67:33. c) Step 1: Determine the composition of one bag of mixture from part (a). In part (a), the mixture was 30 bags of Wairimu and 50 bags of Yellow Green. Total parts = 30+50 = 80. Fraction of Wairimu in mixture (a) = (30)/(80) = (3)/(8). Fraction of Yellow Green in mixture (a) = (50)/(80) = (5)/(8). So, one bag of mixture (a) contains (3)/(8) units of Wairimu and (5)/(8) units of Yellow Green. Step 2: Determine the composition of one bag of mixture from part (b). In part (b), the ratio of Wairimu to Yellow Green is a:b = 67:33. Total parts = 67+33 = 100. Fraction of Wairimu in mixture (b) = (67)/(100). Fraction of Yellow Green in mixture (b) = (33)/(100). So, one bag of mixture (b) contains (67)/(100) units of Wairimu and (33)/(100) units of Yellow Green. Step 3: Calculate the total amount of Wairimu and Yellow Green in the new mixture (one bag from (a) + one bag from (b)). Total Wairimu = (Wairimu from bag (a)) + (Wairimu from bag (b)) Total Wairimu = (3)/(8) + (67)/(100) To add these fractions, find a common denominator, which is 200. Total Wairimu = (3 × 25)/(8 × 25) + (67 × 2)/(100 × 2) = (75)/(200) + (134)/(200) = (209)/(200) Total Yellow Green = (Yellow Green from bag (a)) + (Yellow Green from bag (b)) Total Yellow Green = (5)/(8) + (33)/(100) Using the common denominator 200: Total Yellow Green = (5 × 25)/(8 × 25) + (33 × 2)/(100 × 2) = (125)/(200) + (66)/(200) = (191)/(200) Step 4: Calculate the ratio of Yellow Green to Wairimu. Ratio (Yellow Green : Wairimu) = (191)/(200) : (209)/(200) Since both fractions have the same denominator, the ratio is simply the ratio of their numerators. Ratio = 191 : 209 The ratio of Yellow Green to Wairimu in this new mixture is 191:209. Send me the next one 📸