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