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Sagot :
Price of one pound of mercury is derived as follows;
[tex]\begin{gathered} Price\text{ of 1lb of merc}=\frac{Cost\text{ of flask}}{Pounds\text{ of merc in the flask}} \\ \text{Price of 1 lb}=\frac{150.50}{76} \\ \text{Price of 1 lb}=1.98 \end{gathered}[/tex]This means 1 pound of mercury costs $1.98
1 pound = 453.6 grams
Therefore;
[tex]\begin{gathered} 1lb=453.6gms \\ 76lb=34,473.6gms \end{gathered}[/tex]The price of 1 gram of mercury would be;
[tex]\begin{gathered} Price\text{ of 1 gram}=\frac{Price\text{ per pound}}{\text{grams in 1 lb}} \\ \text{Price of 1 gram}=\frac{1.98}{453.6} \\ \text{Price of 1 gram}=0.004365 \end{gathered}[/tex]This means 1 gram of mercury costs $0.004365
Note that you have 13.534 grams per cubic centimeter of mercury. Therefore, the price of 1 cubic centimeter of mercury shall be calculated as follows;
[tex]\begin{gathered} \text{Price of 1 cubic cm}=grams\text{ per cubic cm x price of 1 gram} \\ \text{price of 1 cubic cm}=13.534\times0.004365 \\ \text{Price of 1 cubic cm}=0.059 \end{gathered}[/tex]This means 1 cubic centimeter of mercury would cost $0.059
Note also that, 1 cubic inch = 16.387 cubic centimeters. Hence,
[tex]\begin{gathered} Price\text{ of 1 cubic inch}=16.387\text{ cubic cm x }price\text{ of 1 cubic cm} \\ \text{Price of 1 cubic inch}=16.387\times0.059 \\ \text{Price of 1 cubic inch}=0.9668 \end{gathered}[/tex]This means 1 cubic inch costs $0.9668
It takes 4.800 cubic inches to make 1 manometer.
Therefore, the cost of 4.800 cubic inches would be;
[tex]\begin{gathered} Price\text{ of 4.800 cubic inches}=Price\text{ of 1 cubic inch x 4.800 cubic inches} \\ Price\text{ of 4.800 cubic inches}=0.9668\times4.800 \\ \text{Price of 4.800 cubic inches}=4.64 \end{gathered}[/tex]If it costs 4.800 cubic inches to make 1 manometer, then the cost of 1 manometer would be $4.64
Therefore, to make 21 manometers, we would have;
[tex]\begin{gathered} 1\text{ manometer}=4.64 \\ 21\text{ manometers}=21\times4.64 \\ 21\text{ manometers}=97.44 \end{gathered}[/tex]ANSWER:
The price of mercury required to make 21 manometers would be $97.44
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