Answer :
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 = [tex]8.32 g/cm^3[/tex]
[tex]V=\frac{M}{D}=\frac{907185 g}{8.32 g/cm^3}=109,036.66 cm^3[/tex]
Volume of copper = v
Volume of zinc = v'
Density of copper = d = [tex]8.96 g/cm^3[/tex]
Density of zinc = d' = [tex]7.14 g/cm^3[/tex]
v + v' = V
[tex]\frac{x}{d}+\frac{y}{d'}=109,036.66 cm^3[/tex]
[tex]\frac{x}{8.96 }+\frac{y}{7.14 }=109,036.66[/tex]...[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
The material cost for making one ton of the brass sample that you have is $4,823.31.
The given parameters;
- density of the copper, = 8.96 g/cm³
- density of the zinc, = 7.14 g/cm³
- density of the brass, = 8.32 g/cm³
- price of zinc, = $1.8/kg
- price of copper = $6.13/kg
The mass of one ton of brass is calculated as follows;
1 ton = 1000 kg = 1,000,000 g
The volume of one ton of brass is calculated as follows;
[tex]V = \frac{m}{\rho } \\\\V = \frac{1,000,000}{8.32} \\\\V = 120,192 .3 \ cm^3[/tex]
The total mass of the copper and zinc is calculated as follows;
[tex]m_c + m_b = 1,000,000\\\\m_c = 1,000,000 - m_b[/tex]
The volume of copper and zinc is calculated as follows;
[tex]\frac{m_c}{\rho } + \frac{m_b}{\rho } = 120,192.3\\\\\frac{m_c}{8.96 } + \frac{m_b}{7.14} = 120,192.3\\\\7.14m_c + 8.96m_b = 7,689,230.27\\\\[/tex]
[tex]7.14(1,000,000 - m_b) + 8.96m_b = 7,689,230.27\\\\7,140,000 - 7.14 m_b + 8.96m_b = 7,689,230.27\\\\1.82 m_b = 549,230.27 \\\\m_b = 301,774.87 \ g = 301.775 \ kg \\\\m_c = 1,000,000 - 301,774.87 = 698,225.13 \ g = 698.225 \ kg[/tex]
The material cost for making one ton of the brass sample that you have.
[tex]cost = 698.225(6.13) \ + \ 301.775(1.8)\\\\cost = \$ 4, 823.31[/tex]
Thus, the material cost for making one ton of the brass sample that you have is $4,823.31.
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