Question

Density of copper is 8.96 g/cm3 and density of zinc is 7.14 g/cm3 . Brass is an alloy made of copper and zinc. You are given a sample of brass with the density of 8.32 g/cm3 . The price of zinc is $1.80/kg and price of copper is $6.13/kg. Determine the material cost for making one ton of the brass sample that you have.

Answer 1

Answer:

$4375.64 is the cost for making one ton of the brass sample of mass 1 Tonn.

Explanation:

Mass of the brass = 1 ton = 907185 g

Mass of copper = x

Mass of zinc = y

x + y = 907185, ....[1]

Volume of the brass = V

Density of the brass = D = $8.32 g/cm^3$

$V=\frac{M}{D}=\frac{907185 g}{8.32 g/cm^3}=109,036.66 cm^3$

Volume of copper = v

Volume of zinc = v'

Density of copper = d = $8.96 g/cm^3$

Density of zinc = d' = $7.14 g/cm^3$

v + v' = V

$\frac{x}{d}+\frac{y}{d'}=109,036.66 cm^3$

$\frac{x}{8.96 }+\frac{y}{7.14 }=109,036.66$...[2]

On solving [1] and [2]:

x = 633,419 g

y = 273,766 g

1 g = 0.001 kg

x = 633,419 g = 633.419 kg

y =  273,766 g = 273.766 kg

The price of zinc = $1.80/kg

Price of 273.766 kg of zinc = $1.80/kg × 273.766 kg = $492.78

The price of copper =  $6.13/kg

Price of 633.419 kg of zinc = $6.13/kg × 633.419 kg = $3882.86

Cost for making one ton of the brass sample :

$492.78 + $3882.86 = $4375.64