99 and 1.83 ,how much should I stake on them to have a loss of 50 naira

Business/Management

ScanSolve AI Answer

Step-by-step solution

6 steps

Let's determine how much to stake on each outcome to achieve a specific loss of 50 naira.

  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

  2. Express stakes in terms of the payout.

    From the payout equations:
    S₁ = P / 1.99
    S₂ = P / 1.83

  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

  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

  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

  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.

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