Can you check my answer?
A business owner is comparing the cost of buying natural gas from two different companies.
Company A charges a $6 fee plus $1.25 per therm (unit of heat).
Company B charges a $9 fee plus $0.75 per therm (unit of heat).
For what number of therms will the cost be the same at both companies?
A. 6 therms
B. 13.5 therms*******
C. 9 therms
D. 12.75 therms
your correct its 13.5
Always check back to your original post
To find the number of therms at which the cost is the same for both companies, we can set up an equation and solve for the variable "therms". Let's go step by step.
From the given information:
Company A charges a $6 fee plus $1.25 per therm.
Company B charges a $9 fee plus $0.75 per therm.
Let's set up the equation:
Cost at Company A = Cost at Company B
The cost at Company A consists of a $6 fee plus $1.25 per therm.
So, the cost at Company A can be expressed as:
Cost at A = 6 + 1.25 * therms
Similarly, the cost at Company B consists of a $9 fee plus $0.75 per therm.
So, the cost at Company B can be expressed as:
Cost at B = 9 + 0.75 * therms
Now, let's set these two expressions equal to each other and solve for therms:
6 + 1.25 * therms = 9 + 0.75 * therms
Let's simplify the equation:
1.25 * therms - 0.75 * therms = 9 - 6
0.5 * therms = 3
Now, divide both sides of the equation by 0.5 to isolate therms:
0.5 * therms / 0.5 = 3 / 0.5
therms = 6
So, the number of therms at which the cost is the same for both companies is 6.
Therefore, the correct answer is A. 6 therms.
6 + 1.25 * 13.5 = 22.875
9 + .75 * 13.5= 19.125
hummm