This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
ScanSolve AI Answer
Let's determine how much to stake on each outcome to achieve a specific loss of 50 naira. Step 1: Define variables and set up the equal payout condition. Let S₁ be the amount staked on the outcome with odds 1.99. Let S₂ be the amount staked on the outcome with odds 1.83. To ensure a consistent loss, the payout must be the same regardless of which outcome wins. Let P be this common payout. P = S₁ × 1.99 P = S₂ × 1.83 Step 2: Express stakes in terms of the payout. From the payout equations: S₁ = P / 1.99 S₂ = P / 1.83 Step 3: Use the desired loss to form an equation. The total money staked is S₁ + S₂. The loss is the total stake minus the payout. We want this loss to be 50 naira. (S₁ + S₂) - P = 50 Step 4: Substitute and solve for the payout (P). Substitute the expressions for S₁ and S₂ into the loss equation: (P / 1.99) + (P / 1.83) - P = 50 Factor out P: P × (1/1.99 + 1/1.83 - 1) = 50 Calculate the values in the parenthesis: 1/1.99 ≈ 0.50251 1/1.83 ≈ 0.54645 P × (0.50251 + 0.54645 - 1) = 50 P × (1.04896 - 1) = 50 P × 0.04896 = 50 P = 50 / 0.04896 P ≈ 1021.24 naira Step 5: Calculate the individual stakes. Now use the value of P to find S₁ and S₂: S₁ = P / 1.99 S₁ = 1021.24 / 1.99 S₁ ≈ 513.19 naira S₂ = P / 1.83 S₂ = 1021.24 / 1.83 S₂ ≈ 558.05 naira Step 6: Verify the total stake and loss. Total stake = S₁ + S₂ = 513.19 + 558.05 = 1071.24 naira Loss = Total stake - Payout = 1071.24 - 1021.24 = 50 naira. This matches the desired loss. To have a loss of 50 naira, you should stake: S₁ = 513.19 naira on the outcome with odds 1.99. S₂ = 558.05 naira on the outcome with odds 1.83. Drop the next question!