Question

The top three prices for works of art sold at auction in 2013 totaled ​$311.4 million. These three works of art were a​ sculpture, a​ painting, and a photograph. The selling price of the painting was ​$51.3 million more than that of the photograph.​ Together, the painting and the photograph sold for ​$22.4 million more than the sculpture. What was the selling price of each​ work?

Answer 1

Price of sculpture = $144.5 million

Price of photograph = $57.8 million

Price of painting = $109.1 million

Step-by-step explanation:

Given:

Total price of 3 arts = $311.4 million

Price of painting + price of photograph + Price of sculpture = $311.4 million ...Eq1

Computation:

We know that,

Price of painting = $51.3 million + price of photograph..........Eq2

Price of painting + price of photograph = $22.4 + Price of sculpture.....Eq 3

From Eq 1 and Eq3,

$22.4 + Price of sculpture + Price of sculpture = $311.4 million

2 Price of sculpture = $289 million

Price of sculpture = $144.5 million

Putting the value of sculpture in Eq1

Price of painting + price of photograph + $144.5 million = $311.4 million

Price of painting + price of photograph = $166.9 million.......Eq4

From Eq2 and Eq4

Price of photograph = $57.8 million

Price of painting = $109.1 million