Choose the inequality that matches this situation.

Question

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 1

Let's define the number of brochures ordered as \( x \).

For Company A, the total cost can be represented as: \[ \text{Cost}_A = 25 + 0.20x \]

For Company B, the total cost is: \[ \text{Cost}_B = 0.30x \]

We want to determine the number of brochures (\( x \)) for which Company A's cost is greater than Company B's cost. This can be expressed with the inequality: \[ 25 + 0.20x > 0.30x \]

Now, we can solve this inequality for \( x \).

Subtract \( 0.20x \) from both sides: \[ 25 > 0.30x - 0.20x \]

This simplifies to: \[ 25 > 0.10x \]

Now, divide both sides by \( 0.10 \): \[ 250 > x \]

Rearranging gives us: \[ x < 250 \]

Thus, the final inequality that describes the situation, indicating how many brochures can be ordered for Company A's cost to be greater than Company B's, is: \[ x < 250 \]