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
Welcome back Champion — been a while! Let's pick up where you left off. a) Option A will possibly be a contract option. Option A has a fixed cost of R150 even when 0 minutes are used, as shown in the table and graph (it starts at R150 on the y-axis). A contract option typically includes a base monthly fee regardless of usage. Option B starts at R0 for 0 minutes, indicating a pay-as-you-go or prepaid structure. b) Step 1: Calculate the tariff per minute for Option A. Using points (0, 150) and (50, 230) from the table: Tariff A = Change in CostChange in Minutes = (230 - 150)/(50 - 0) = (80)/(50) = 1.6 The tariff for Option A is R1.60 per minute. Step 2: Calculate the tariff per minute for Option B. Using points (0, 0) and (50, 125) from the table: Tariff B = Change in CostChange in Minutes = (125 - 0)/(50 - 0) = (125)/(50) = 2.5 The tariff for Option B is R2.50 per minute. c) Step 1: Write the equation for Option A. The general form is C = mM + c, where C is total cost, M is minutes, m is the tariff per minute, and c is the fixed cost. For Option A, m = 1.6 and c = 150. C_A = 1.6M + 150 Step 2: Write the equation for Option B. For Option B, m = 2.5 and c = 0. C_B = 2.5M d) Step 1: Calculate the cost for Option A for 100 minutes. Substitute M = 100 into the equation for Option A: C_A = 1.6(100) + 150 = 160 + 150 = 310 The cost for Option A is R310. Step 2: Calculate the cost for Option B for 100 minutes. Substitute M = 100 into the equation for Option B: C_B = 2.5(100) = 250 The cost for Option B is R250. Step 3: Compare the costs. Since R250 < R310, Option B will be the cheapest option for 100 minutes of calls. e) Step 1: Set the costs equal to find the intersection point. Option A becomes cheaper than Option B when C_A < C_B. The point where they are equal is the intersection: 1.6M + 150 = 2.5M Step 2: Solve for M. 150 = 2.5M - 1.6M 150 = 0.9M M = (150)/(0.9) = (1500)/(9) ≈ 166.67 So, approximately 167 minutes. Step 3: Calculate the cost at this number of minutes. Using M ≈ 166.67 in either equation: C_B = 2.5(166.67) ≈ 416.675 At approximately (167 minutes, 417 R), Option A becomes cheaper than Option B. Send me the next one 📸