Farm A has a 100 ft well that uses 7,000 cubic feet of natural gas per year. If the cost of natural gas is $2.50 per 1,000 cubic feet, what is the annual cost to operate this well?

Answer 1

Hi! For this problem, you will have to use dimensional analysis and unit conversions to determine the annual cost of operation, based on the size of the well and the cost of natural gas per unit area.

Step 1: Convert usage to thousands of cubic feet

First, based on the information the problem provides us with, we know that natural gas is priced in “chunks” of 1,000 cubic feet, and that Farm A uses 7,000 cubic feet per year. To find out how many of those 1,000 cubic feet “chunks” they use, we will divide 7,000 by 1,000, which gives us 7.

Mathematically, we can express this as:

7,000 cubic feet / 1,000 cubic feet per “chunk” = 7 “chunks” of 1,000 cubic feet

(The cubic feet units in the numerator and denominator cancel, leaving us with “chunks” as our unit, and 7 as our numerical answer)

Step 2: Multiply by the cost per unit

Based on our work for part 1, we determined that Farm A uses 7 “chunks” of 1,000 cubic feet sections, for a total of 7,000 cubic feet. According to the problem, it costs $2.50 for 1,000 cubic feet to receive natural gas. Since Farm A uses 7 of these 1,000 cubic feet chunks, we multiply 7 by $2.50, for a total of $17.50.

Mathematically, we can model this problem as:

(7,000 ft³ / 1000 ft³ per chunk) x $2.50 per chunk = $17.50

(7,000 ft³ / 1000 ft³ per chunk) x $2.50 per chunk = $17.50

7 chunks x $2.50 per chunk = $17.50

7 chunks x $2.50 per chunk = $17.50

(Through division, the ft² units cancel, leaving us with “chunks.” When we multiply by $2.50 per “chunk,” “chunks” also cancel, leaving us with $ as our final remaining unit)

Therefore, it will cost $17.50 annually to operate Farm A’s well.