Question
Company charges 312$ plus 12$ per window . Company B charges 36$ per window . How many windows must a house have to make the total cost from comp at A less expensive than company B
Answers
GPT-4o mini
To find out how many windows must a house have for Company A to be less expensive than Company B, we can set up the cost equations for both companies and then compare them.
Let \( x \) be the number of windows.
The total cost for Company A is:
\[ C_A = 312 + 12x \]
The total cost for Company B is:
\[ C_B = 36x \]
We want to find when Company A's cost is less than Company B's cost:
\[ 312 + 12x < 36x \]
Now, we can solve this inequality:
1. Subtract \( 12x \) from both sides:
\[ 312 < 36x - 12x \]
\[ 312 < 24x \]
2. Divide both sides by 24:
\[ \frac{312}{24} < x \]
\[ 13 < x \]
This means that \( x > 13 \).
Therefore, a house must have more than **13 windows** for Company A to be less expensive than Company B.
Let \( x \) be the number of windows.
The total cost for Company A is:
\[ C_A = 312 + 12x \]
The total cost for Company B is:
\[ C_B = 36x \]
We want to find when Company A's cost is less than Company B's cost:
\[ 312 + 12x < 36x \]
Now, we can solve this inequality:
1. Subtract \( 12x \) from both sides:
\[ 312 < 36x - 12x \]
\[ 312 < 24x \]
2. Divide both sides by 24:
\[ \frac{312}{24} < x \]
\[ 13 < x \]
This means that \( x > 13 \).
Therefore, a house must have more than **13 windows** for Company A to be less expensive than Company B.