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 system of equations using the substitution method: Step 1: Express one variable in terms of the other from one of the equations. We have the system: 1) 3p + 2e = 190 2) 2p + 5e = 290 From equation (1), let's express e in terms of p: 2e = 190 - 3p e = (190 - 3p)/(2) Step 2: Substitute this expression into the other equation. Substitute the expression for e from Step 1 into equation (2): 2p + 5((190 - 3p)/(2)) = 290 Step 3: Solve the resulting single-variable equation 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) Step 4: Substitute the value of p back into the expression for e from Step 1. e = (190 - 3p)/(2) Substitute p = (370)/(11): e = (190 - 3(370)/(11))2 e = (190 - 1110)/(11)2 Find a common denominator for the terms in the numerator: 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 pencil is KSh (370)/(11) and the cost of one exercise book is KSh (490)/(11). That's 2 down. 3 left today — send the next one.