Choose the inequality that matches this situation..

Question

Company A charges $312 to power-wash the siding of a house plus $12 for each window. Company B charges $36 per window, and the price includs 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

To determine how many windows must a house have for Company A to be less expensive than Company B, we can set up inequalities based on the pricing models of both companies.

Let's denote the number of windows as \( w \).

• Cost from Company A: This cost is \( 312 + 12w \) (where $312 is the base charge for power-washing the siding and $12 is the cost per window).

• Cost from Company B: This cost is \( 36w \) (where $36 per window assumes the price includes the siding).

We want to find when Company A's cost is less than Company B's cost:

\[ 312 + 12w < 36w \]

Now, we can solve the inequality:

1. Subtract \( 12w \) from both sides: \[ 312 < 36w - 12w \] \[ 312 < 24w \]

2. Divide both sides by 24: \[ \frac{312}{24} < w \] \[ 13 < w \]

This means \( w > 13 \).

Therefore, the number of windows must be greater than 13 for Company A to be less expensive than Company B. The correct inequality is:

\[ w > 13 \]

Answer 2

Choose the inequality that matches this situation.
Company A charges a fee of $25 plus $0.20 per brouchure to print and deliver them. Company B charges $0.30 per brochure. How many would need to be ordered for Company A to cost more than Company B?

Answer 3

To determine how many brochures need to be ordered for Company A to cost more than Company B, we can set up inequalities based on the pricing models provided.

Let \( b \) represent the number of brochures ordered.

• Cost from Company A: This cost is given by the formula: \[ \text{Cost}_A = 25 + 0.20b \] (where $25 is the fixed fee plus $0.20 per brochure).

• Cost from Company B: This cost is given by the formula: \[ \text{Cost}_B = 0.30b \] (where $0.30 is the cost per brochure).

We want to find when Company A's cost is more than Company B's cost:

\[ 25 + 0.20b > 0.30b \]

Now, we can solve the inequality:

1. Subtract \( 0.20b \) from both sides: \[ 25 > 0.30b - 0.20b \] \[ 25 > 0.10b \]

2. Divide both sides by 0.10: \[ \frac{25}{0.10} > b \] \[ 250 > b \]

This means that for Company A to cost more than Company B, the number of brochures ordered must be less than 250. The correct inequality is:

\[ b < 250 \]