Question

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

Answer 1

Kay will save approximately $319.82 by burning gas instead of wood in one winter.

Step-by-step explanation:

To calculate how much Kay will save by burning gas instead of wood, we need to compare the costs of burning each fuel.

To burn wood, Kay normally uses 2 cords, at a cost of $250 per cord. This means she spends 2 * $250 = $500 on wood in the winter.

Next, we need to calculate the cost of burning gas. The fireplace insert burns 33,000 BTU per hour and Kay will burn the fireplace for 5 hours per day for 120 days. This is a total of 33,000 * 5 * 120 = 19,800,000 BTU in one winter.

Since 1 therm is 100,000 BTU, Kay will burn 19,800,000 / 100,000 = 198 therms of gas.

The cost of gas is $0.91 per therm, so Kay will spend 198 * $0.91 = $180.18 on gas in the winter.

To calculate her savings, we subtract the cost of gas from the cost of wood: $500 - $180.18 = $319.82.

Kay will save approximately $319.82 by burning gas instead of wood in one winter.

Answer 2

Saved Money = $ 319.82

Step-by-step explanation:

First, we will calculate the cost of wood:

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

Now, we calculate the time to burn gas:

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

Now, we calculate the energy:

`Energy\ Required = (600\ hr)(33000\ BTU/hr)((1\ therm)/(100000\ BTU))\\\\Energy\ Required = 198\ therm\\`

Now, we will calculate the cost of gas:

`Gas\ Cost = (Energy\ Required)(Unit\ Cost)\\Gas\ Cost = (198\ therm)(\$\ 0.91/therm)\\Gas\ Cost = \$\ 180.18\\`

Now, we will calculate the amount of money saved:

`Saved\ Money = Wood\ Cost - Gas\ Cost\\Saved\ Money = \$\ 500 - \$\ 180.18\\`

Saved Money = $ 319.82