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

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.