Company B charges less for 125 cubic feet of natural gas.
Company B charges $0.25 less than Company A for 125 cubic feet of natural gas.
How to know which company charges less
To know which company charges less, follow this steps
Step 1: Calculate the cost for Company A for 125 cubic feet of natural gas.
Since the cost for Company A is not given directly for 125 cubic feet, interpolate between the provided values in the table.
Based on the table, the cost for 75 cubic feet is $37.50 and the cost for 110 cubic feet is $55.0
Assume a linear relationship between these two points and use the slope-intercept form to represent the cost for Company A:
y = mx + b
where:
m is the slope
b is the y-intercept
To find the slope (m), we can use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) = (75, 37.50) and (x₂, y₂) = (110, 55.00)
m = (55.00 - 37.50) / (110 - 75) = 0.5
Now substitute the slope (m = 0.5) and one of the data points (x = 75, y = 37.50) into the equation to find the y-intercept (b):
37.50 = 0.5 * 75 + b
b = 37.50 - 37.50
b = 0
Therefore, the equation for the cost of natural gas for Company A is:
y = 0.5x
Step 2: Calculate the cost for Company B for 125 cubic feet of natural gas.
For Company B, the cost can be represented by the equation:
y = 0.53x
Substituting x = 125 into this equation
y = 0.53 * 125
y = 66.25
For Company A, the cost can be represented by the equation:
y = 0.5x
Substituting x = 125 into this equation
y = 0.5 * 125
y = 66.5
Step 3: Compare the costs and determine the less expensive company.
Comparing the costs for both companies, we have:
Company A: y = 66.5
Company B: y = 66.25
Therefore, Company B charges less for 125 cubic feet of natural gas. The difference in cost is:
Difference in cost = Company B's cost - Company A's cost
Difference in cost = 66.5 - 66.25
Difference in cost = 0.25
Hence, Company B charges $0.25 less than Company A for 125 cubic feet of natural gas.
Isabella is comparing rates for two natural gas companies. For Company A, the cost y for x cubic feet of natural gas is shown in the table. For Company B, the cost y can be represented by the equation y=0.53x, , where x represents the number of cubic feet. Which company charges less for 125 cubic feet of natural gas? How much less?
number of cubic feet, x Total cost ($), y
75 37.50
110 55.00