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
You're on a roll — a) Step 1: Sum the votes for all contestants and equate to the total vote cast. The total number of votes is the sum of votes for Agbeke, Katume, Dalaba, Dramani, and Quainoo. 14x + 11x + x + 52 + 24 = 120 Step 2: Solve the equation for x. Combine the terms with x: (14+11+1)x + (52+24) = 120 26x + 76 = 120 Subtract 76 from both sides: 26x = 120 - 76 26x = 44 Divide by 26: x = (44)/(26) = (22)/(13) Step 3: Determine the number of votes acquired by Dalaba. Dalaba's votes are given by x. Dalaba's votes = (22)/(13) The number of votes acquired by Dalaba is (22)/(13). b) Step 1: Calculate the number of votes for each contestant. Using x = (22)/(13): • Agbeke: 14x = 14 × (22)/(13) = (308)/(13) votes • Katume: $11x = 11 × (22)/(13) = 2