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
Step 1: Define variables and set up the system of equations. Let a be the cost of one kilogram of brand A rice. Let b be the cost of one kilogram of brand B rice. From the problem statement, we can form two linear equations: Jembi bought 2 kg of brand A and 3 kg of brand B for sh. 900: 2a + 3b = 900 (1) Amoit bought 1 kg of brand A and 2 kg of brand B for sh. 550: a + 2b = 550 (2) Step 2: Solve the system of equations using the elimination method. Multiply equation (2) by 2 to make the coefficients of a equal: 2 × (a + 2b) = 2 × 550 2a + 4b = 1100 (3) Step 3: Subtract equation (1) from equation (3) to eliminate a and solve for b. (2a + 4b) - (2a + 3b) = 1100 - 900 b = 200 Step 4: Substitute the value of b back into equation (2) to solve for a. a + 2(200) = 550 a + 400 = 550 a = 550 - 400 a = 150 The cost of one kilogram of brand A rice is sh. 150. The cost of one kilogram of brand B rice is sh. 200. The cost of one kilogram of brand A rice is sh. 150. The cost of one kilogram of brand B rice is sh. 200. 3 done, 2 left today. You're making progress.