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 questions 12, 13, and 14: 12. The cost of 2 bags of maize and 3 bags of beans is Ksh 12,500. The cost of 3 bags of maize and 5 bags of beans is Ksh 20,000. Find the cost of one bag of each item. Step 1: Formulate simultaneous equations. Let m be the cost of one bag of maize and b be the cost of one bag of beans. From the given information: 2m + 3b = 12,500 (1) 3m + 5b = 20,000 (2) Step 2: Solve the equations using the elimination method. Multiply equation (1) by 3 and equation (2) by 2 to eliminate m: 3 × (2m + 3b) = 3 × 12,500 6m + 9b = 37,500 (3) 2 × (3m + 5b) = 2 × 20,000 6m + 10b = 40,000 (4) Step 3: Subtract equation (3) from equation (4) to find b. (6m + 10b) - (6m + 9b) = 40,000 - 37,500 b = 2,500 Step 4: Substitute the value of b into equation (1) to find m. 2m + 3(2,500) = 12,500 2m + 7,500 = 12,500 2m = 12,500 - 7,500 2m = 5,000 m = 2,500 The cost of one bag of maize is Ksh. 2,500 and the cost of one bag of beans is Ksh. 2,500. 13. Given the column vectors: a = 2 \\ -3 , b = 5 \\ 1 , c = -4 \\ 6 . Find |3a + b - c|. Step 1: Calculate 3a. 3a = 3 2 \\ -3 = 3 × 2 \\ 3 × (-3) = 6 \\ -9 Step 2: Calculate 3a + b. 3a + b = 6 \\ -9 + 5 \\ 1 = 6 + 5 \\ -9 + 1 = 11 \\ -8 Step 3: Calculate 3a + b - c. 3a + b - c = 11 \\ -8 - -4 \\ 6 = 11 - (-4) \\ -8 - 6 = 11 + 4 \\ -14 = 15 \\ -14 Step 4: Find the magnitude (modulus) of the resulting vector. |3a + b - c| = | 15 \\ -14 | = sqrt(15^2 + (-14)^2) = sqrt(225 + 196) = sqrt(421) |3a + b - c| = sqrt(421) 14. A Kenyan bank buys and sells foreign currency as follows: | Currency | Buying (Ksh) | Selling (Ksh) | |---|---|---| | 1 US Dollar | 129.50 | 130.70 | | 1 Euro | 135.20 | 136.50 | A tourist arrives with 5,000 Euros and 2,000 US Dollars. He changes all the money to Kenya Shillings. How much does he receive? Step 1: Determine the exchange rate to use. Since the tourist is changing foreign currency to Kenya Shillings, the bank is buying the foreign currency from the tourist. Therefore, we use the "Buying (Ksh)" rates. Step 2: Calculate the amount received from changing Euros. Amount from Euros = 5,000 Euros × 135.20 Ksh/Euro Amount from Euros = 676,000 Ksh Step 3: Calculate the amount received from changing US Dollars. Amount from US Dollars = 2,000 USD × 129.50 Ksh/USD Amount from US Dollars = 259,000 Ksh Step 4: Calculate the total amount received in Kenya Shillings. Total Amount = Amount from Euros + Amount from US Dollars Total Amount = 676,000 + 259,000 Total Amount = Ksh. 935,000 Got more? Send 'em!