Final answer:
The selling price of the sculpture is $144.4 million, the painting is $106.5 million, and the photograph is $56.4 million.
Step-by-step explanation:
Let's represent the selling price of the sculpture, painting, and photograph as S, P, and Ph respectively.
From the given information, we can set up the following equations:
1. P + Ph + S = 307.3 million
2. P = Ph + 50.1 million
3. (P + Ph) - S = 18.5 million
Using equation 2, we can substitute the value of P in equations 1 and 3 to solve for Ph and S.
Substituting P = Ph + 50.1 million into equation 1, we get:
(Ph + 50.1 million) + Ph + S = 307.3 million
2Ph + S = 307.3 million - 50.1 million
2Ph + S = 257.2 million
Now, substituting P = Ph + 50.1 million into equation 3, we get:
(Ph + 50.1 million + Ph) - S = 18.5 million
2Ph + 50.1 million - S = 18.5 million
2Ph - S = 18.5 million - 50.1 million
2Ph - S = -31.6 million
We now have a system of two equations with two variables:
2Ph + S = 257.2 million
2Ph - S = -31.6 million
Let's solve this system using elimination method:
Add the two equations:
(2Ph + S) + (2Ph - S) = 257.2 million + (-31.6 million)
4Ph = 225.6 million
Divide both sides by 4:
Ph = 56.4 million
Substituting the value of Ph into equation 2:
P = 56.4 million + 50.1 million
P = 106.5 million
Substituting the values of P and Ph back into equation 1:
P + Ph + S = 307.3 million
106.5 million + 56.4 million + S = 307.3 million
162.9 million + S = 307.3 million
S = 307.3 million - 162.9 million
S = 144.4 million
Therefore, the selling price of the sculpture is $144.4 million, the painting is $106.5 million, and the photograph is $56.4 million.