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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You're on a roll — Here's the solution to question 3: Let x be the cost of one textbook and y be the cost of one exercise book. Step 1: Formulate equations based on the given information. For Elimu school: 25 textbooks and 35 exercise books cost sh. 13500. 25x + 35y = 13500 (Equation 1) For Soma school: Soma school bought 21 textbooks and 38 exercise books. They spent sh. 1300 less than Elimu school. Elimu school spent sh. 13500, so Soma school spent 13500 - 1300 = 12200 sh. 21x + 38y = 12200 (Equation 2) Step 2: Solve the system of linear equations using the elimination method. Multiply Equation 1 by 21 and Equation 2 by 25 to eliminate x. Equation 1 × 21: 21(25x) + 21(35y) = 21(13500) 525x + 735y = 283500 (Equation 3) Equation 2 × 25: 25(21x) + 25(38y) = 25(12200) 525x + 950y = 305000 (Equation 4) Step 3: Subtract Equation 3 from Equation 4 to solve for y. (525x + 950y) - (525x + 735y) = 305000 - 283500 215y = 21500 y = (21500)/(215) y = 100 The cost of one exercise book is sh. 100. Step 4: Substitute the value of y into Equation 1 to solve for x. 25x + 35(100) = 13500 25x + 3500 = 13500 25x = 13500 - 3500 25x = 10000 x = (10000)/(25) x = 400 The cost of one textbook is sh. 400. The cost of one textbook is sh. 400. The cost of one exercise book is sh. 100. Just 1 left today. What's next?