Question

During one month, a homeowner used 400 units of electricity and 100 units of gas for a total cost of $256. The next month, 300 units of electricity and 250 units of gas were used for a total cost of $241. Find the cost per unit of gas.

Answer 1

By setting up a system of linear equations from the given data and solving it, the cost per unit of gas is determined to be $0.28.

Step-by-step explanation:

The cost per unit of gas can be found by setting up a system of equations based on the information given. Let e be the cost per unit of electricity and g be the cost per unit of gas.

For the first month, the equation based on the usage and cost is:
400e + 100g = $256

For the second month, the equation is:
300e + 250g = $241

We have two equations with two unknowns, which can be solved using the substitution or elimination method. As an example, using elimination method:

• Multiply the first equation by 3 and the second by 4 to align the e terms:
  1200e + 300g = $768
  1200e + 1000g = $964
• Now subtract the first new equation from the second:
  700g = $196
• We can now find g by dividing both sides by 700:
  g = $196 / 700
• This gives us the cost per unit of gas:
  g = $0.28 per unit.

Therefore, the cost per unit of gas is $0.28.