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ay wants to buy a new fireplace insert that will burn gas instead of wood. She normally uses two cords of wood in the winter. Wood costs $250/cord. She is interested in knowing how much she will save if she burns gas in the fireplace insert. Gas costs $0.91 per therm. One therm is 100,000 BTU. The fireplace insert burns 33,000 BTU per hour. Kay figures she will burn the fireplace 5 hours per day for 120 days. How much will she save in one winter if she burns gas instead of wood

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hamzaahmeds

Answer:

Saved Money = $ 319.82

Explanation:

First, we will calculate the cost of wood:

[tex]Wood\ Cost = (No.\ of\ Cords)(Unit\ Cost)\\Wood\ Cost = (2 cords)(\$ 250/cord)\\Wood\ Cost = \$ 500\\[/tex]

Now, we calculate the time to burn gas:

[tex]Time\ to\ burn\ gas = (5\ hours/day)(120\ days)\\Time\ to\ burn\ gas = 600\ hr\\[/tex]

Now, we calculate the energy:

[tex]Energy\ Required = (600\ hr)(33000\ BTU/hr)(\frac{1\ therm}{100000\ BTU})\\\\Energy\ Required = 198\ therm\\[/tex]

Now, we will calculate the cost of gas:

[tex]Gas\ Cost = (Energy\ Required)(Unit\ Cost)\\Gas\ Cost = (198\ therm)(\$\ 0.91/therm)\\Gas\ Cost = \$\ 180.18\\[/tex]

Now, we will calculate the amount of money saved:

[tex]Saved\ Money = Wood\ Cost - Gas\ Cost\\Saved\ Money = \$\ 500 - \$\ 180.18\\[/tex]

Saved Money = $ 319.82

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