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
Here's how to solve the problem: Step 1: Set up the system of equations. Let p be the cost of one pencil and e be the cost of one exercise book. From the problem statement, we have: 1. Two exercise books and three pencils cost KSh 190: 3p + 2e = 190 (1) 2. Five similar exercise books and two similar pencils cost KSh 290: 2p + 5e = 290 (2) The student has already started by expressing e from equation (1): 2e = 190 - 3p e = (190 - 3p)/(2) Step 2: Substitute the expression for e into equation (2). Substitute e = (190 - 3p)/(2) into 2p + 5e = 290: 2p + 5((190 - 3p)/(2)) = 290 Step 3: Solve for p. Multiply the entire equation by 2 to eliminate the fraction: 2(2p) + 2 · 5((190 - 3p)/(2)) = 2(290) 4p + 5(190 - 3p) = 580 4p + 950 - 15p = 580 -11p + 950 = 580 -11p = 580 - 950 -11p = -370 p = (-370)/(-11) p = (370)/(11) The cost of one pencil is KSh (370)/(11). Step 4: Substitute the value of p back into the expression for e. e = (190 - 3p)/(2) e = (190 - 3(370)/(11))2 e = (190 - 1110)/(11)2 To simplify the numerator, find a common denominator: e = (190 × 11)/(11) - (1110)/(11)2 e = (2090)/(11) - (1110)/(11)2 e = (2090 - 1110)/(11)2 e = (980)/(11)2 e = (980)/(11 × 2) e = (980)/(22) e = (490)/(11) The cost of one exercise book is KSh (490)/(11). The cost of one pencil is KSh (370)/(11) and the cost of one exercise book is KSh (490)/(11). Send me the next one 📸