Choose the inequality company a charges a fee of $25 plus 0.20 per brochure 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

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

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

Company A charges a fee of $25 plus $0.20 per brochure. Therefore, the cost for Company A can be expressed as: \[ \text{Cost}_A = 25 + 0.20x \]

Company B charges $0.30 per brochure. Therefore, the cost for Company B is: \[ \text{Cost}_B = 0.30x \]

We want to find when Company A costs more than Company B: \[ 25 + 0.20x > 0.30x \]

Now, let's solve this inequality step by step:

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

  2. Divide both sides by \( 0.10 \) to solve for \( x \): \[ \frac{25}{0.10} > x \] \[ 250 > x \] or \[ x < 250 \]

This means that Company A will cost more than Company B when the number of brochures \( x \) is less than 250. In other words, for any order of brochures less than 250, Company A will be the more expensive option.