99 and 1.83 ,how much should I stake on them to have a loss of 50 naira
ScanSolve AI Answer
Step-by-step solution
6 stepsLet's determine how much to stake on each outcome to achieve a specific loss of 50 naira.
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 × 1.83Express stakes in terms of the payout.
From the payout equations:
S₁ = P / 1.99
S₂ = P / 1.83Use 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 = 50Substitute 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 nairaCalculate 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 nairaS₂ = P / 1.83
S₂ = 1021.24 / 1.83
S₂ ≈ 558.05 nairaVerify 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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