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

Answer 1

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.