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 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:

312 - 12w > 36w

312 + 12w < 36w

12w + 36w > 312

36w - 12w < 312

Answer 1

To determine the inequality that represents the situation, let's define \( w \) as the number of windows.

1. Cost of Company A: The cost is $312 for the siding plus $12 for each window. Therefore, the total cost for Company A can be expressed as: \[ C_A = 312 + 12w \]

2. Cost of Company B: The cost is $36 for each window, and this price includes the siding. Therefore, the total cost for Company B can be expressed as: \[ C_B = 36w \]

We want to find the number of windows \( w \) for which the cost from Company A is less expensive than the cost from Company B. This can be expressed with the inequality: \[ C_A < C_B \] Substituting in the expressions for \( C_A \) and \( C_B \): \[ 312 + 12w < 36w \]

Now we simplify the inequality:

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

2. Rearranging gives: \[ 312 < 24w \quad \text{or} \quad 312 > 24w \quad \text{(reversing the inequality)} \]

To express it in the form that matches one of the given answers:

\[ 312 + 12w < 36w \]

The correct answer from the choices provided is: \[ \boxed{312 + 12w < 36w} \]

Answer 2

are you sure

Answer 3

Let's carefully verify the problem and the derived inequality step-by-step to confirm the right inequality that matches the situation.

Given Information:

1. Company A:

   • Charges $312 for power-washing the siding of a house.
   • Charges $12 for each window.
   • Total cost for Company A: \[ C_A = 312 + 12w \]

2. Company B:

   • Charges $36 per window, which includes siding.
   • Total cost for Company B: \[ C_B = 36w \]

We need to find when Company A is less expensive than Company B:

This can be expressed as: \[ C_A < C_B \] \[ 312 + 12w < 36w \]

Simplifying the inequality:

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

2. Rearranging gives: \[ 312 < 24w \quad \text{or} \quad 312 > 24w \quad \text{(reversed)} \]

So indeed, the inequality derived correctly is: \[ 312 + 12w < 36w \]

Review of Given Answers:

The available answer that matches this situation is: \[ \boxed{312 + 12w < 36w} \]

This is confirmed to be correct. Therefore, my initial answer is accurate. Thank you for prompting the clarification!