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