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Cake day: August 28th, 2023

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  • Let’s denote the prices of the components as follows:

    Egg: ( E )

    Bacon: ( B )

    Sausage: ( S )

    Spam: ( P )

    We are given the following equations based on the prices of the combinations:

    ( E + B = 1.10 )

    ( E + S + B = 1.49 )

    ( E + P = 1.50 )

    ( E + P + B = 2.10 )

    ( E + P + S + B = 2.49 )

    First, subtract Equation 1 from Equation 2:

    [ (E + S + B) - (E + B) = 1.49 - 1.10 ]

    [ S = 0.39 ]

    Next, subtract Equation 1 from Equation 4:

    [ (E + P + B) - (E + B) = 2.10 - 1.10 ]

    [ P = 1.00 ]

    Next, subtract Equation 3 from Equation 5:

    [ (E + P + S + B) - (E + P) = 2.49 - 1.50 ]

    [ S + B = 0.99 ]

    We already know from a previous calculation that ( S = 0.39 ), so substitute ( S ) in:

    [ 0.39 + B = 0.99 ]

    [ B = 0.60 ]

    Now we know ( B ) and can find ( E ) from Equation 1:

    [ E + 0.60 = 1.10 ]

    [ E = 0.50 ]

    We have found the prices:

    Egg (( E )) = 0.50

    Bacon (( B )) = 0.60

    Sausage (( S )) = 0.39

    Spam (( P )) = 1.00