Question
Choose the inequality company a charges $312 power wash the siding of a house plus 12 for each window company b charges 36 per window and the price includes the siding how many windows must a house have to make the total cost from company a be less expensive than company b
Answers
GPT-4o mini
Let's denote the number of windows in the house as \( x \).
For Company A, the total cost \( C_A \) is given by:
\[
C_A = 312 + 12x
\]
For Company B, the total cost \( C_B \) is given by:
\[
C_B = 36x
\]
To find out when Company A's cost is less than Company B's, we need to set up the inequality:
\[
312 + 12x < 36x
\]
Now, let's solve this inequality:
1. Subtract \( 12x \) from both sides:
\[
312 < 36x - 12x
\]
2. Simplify the right side:
\[
312 < 24x
\]
3. Divide both sides by 24:
\[
\frac{312}{24} < x
\]
4. Calculate \( \frac{312}{24} \):
\[
\frac{312}{24} = 13
\]
Thus, the inequality simplifies to:
\[
x > 13
\]
This means the house must have **more than 13 windows** for Company A to be less expensive than Company B. Therefore, if the house has at least **14 windows**, Company A will be the cheaper option.
For Company A, the total cost \( C_A \) is given by:
\[
C_A = 312 + 12x
\]
For Company B, the total cost \( C_B \) is given by:
\[
C_B = 36x
\]
To find out when Company A's cost is less than Company B's, we need to set up the inequality:
\[
312 + 12x < 36x
\]
Now, let's solve this inequality:
1. Subtract \( 12x \) from both sides:
\[
312 < 36x - 12x
\]
2. Simplify the right side:
\[
312 < 24x
\]
3. Divide both sides by 24:
\[
\frac{312}{24} < x
\]
4. Calculate \( \frac{312}{24} \):
\[
\frac{312}{24} = 13
\]
Thus, the inequality simplifies to:
\[
x > 13
\]
This means the house must have **more than 13 windows** for Company A to be less expensive than Company B. Therefore, if the house has at least **14 windows**, Company A will be the cheaper option.