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Choose the inequality that matches this situation.

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?
312-12w > 36w
312+12w <36w
12w+36w > 312
36w-12w< 312

1 answer

To determine the inequality that matches the situation, we need to break down the costs for both companies based on the number of windows, represented by \( w \).

Company A's cost:

  • Charges $312 for power-washing the siding.
  • Charges $12 for each window.
  • Therefore, the total cost for Company A is given by: \[ 312 + 12w \]

Company B's cost:

  • Charges $36 for each window.
  • The price includes the siding, so the total cost for Company B is: \[ 36w \]

We want to find when Company A's cost is less than Company B's cost: \[ 312 + 12w < 36w \]

To simplify, we subtract \( 12w \) from both sides: \[ 312 < 36w - 12w \] \[ 312 < 24w \]

This leads us to the inequality: \[ \frac{312}{24} < w \] which simplifies to: \[ w > 13 \]

So, we need to find the inequality form corresponding to this situation.

The correct answer is: \[ 312 + 12w < 36w \]

Thus, the correct option is: 312 + 12w < 36w.