Question

During one month, a homeowner used 400 units of electricity and 100 units of gas for a total cost of $288. The next month, 300 units of electricity and 150 units of gas were used for a total cost of $240. Find the cost per unit of gas.

a) $1.50
b) $1.60
c) $1.80
d) $2.00

Answer 1

The question requires solving a system of linear equations to find the cost per unit of gas. By setting up the equations and using the elimination method, we calculate the cost per unit of gas. However, the calculated value does not match the provided options, indicating a possible error in the information presented.

Step-by-step explanation:

The question involves solving a system of linear equations to determine the cost per unit of gas.

Let's denote the cost per unit of electricity as E and the cost per unit of gas as G. From the given data, we have two equations:

Now we can solve this system using methods like substitution or elimination. If we decide to solve it by elimination, we can multiply the first equation by 3 and the second by 4 to eliminate E:

1200E + 300G = $864 (First equation multiplied by 3)

1200E + 600G = $960 (Second equation multiplied by 4)

Subtract the first modified equation from the second modified equation:

1200E + 600G - (1200E + 300G) = $960 - $864

300G = $96

Divide both sides by 300 to find the cost per unit of gas:

G = $0.32 per unit

However, this is not matching any of the options given in the question, which suggests there may have been a mistake in the calculations or in the provided options. Since we are unsure of the correctness due to the options listed, we must abstain from confidently providing an answer in this scenario.