Question

During one month, a homeowner used 600 units of electricity and 100 units of gas for a total cost of $344. The next month, 400 units of electricity and 250 units of gas were used for a total cost of $299. Find the cost per unit of gas.

Answer 1

Answer: the cost per unit of gas is $0.38

Step-by-step explanation:

Let x represent the cost per unit of electricity.

Let y represent the cost per unit of gas.

During one month, a homeowner used 600 units of electricity and 100 units of gas for a total cost of $344. It means that

600x + 100y = 344- - - - - - - - - -1

The next month, 400 units of electricity and 250 units of gas were used for a total cost of $299.

It means that

400x + 250y = 299- - - - - - - - - -1

Multiplying equation 1 by 400 and equation 2 by 600, it becomes

240000x + 40000y = 137600

240000x + 150000y = 179400

Subtracting, it becomes

- 110000y = - 41800

y = - 41800/- 110000

y = 0.38

Substituting y = 0.38 into equation 1, it becomes

600x + 100 × 0.38 = 344

600x + 38 = 344

600x = 344 - 38 = 306

x = 306/600

x = 0.51