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?

Question

$0.20b + $0.30b > 25b

$0.20b + $0.30b < 25b

$25 + $0.20b > $0.30b

$25 + $0.20b < $0.30b

Answer 1

To determine how many brochures need to be ordered for Company A to cost more than Company B, we can set up an inequality based on their costs.

Let \( b \) represent the number of brochures.

1. The cost for Company A is: \[ \text{Cost}_A = 25 + 0.20b \]

2. The cost for Company B is: \[ \text{Cost}_B = 0.30b \]

To find when Company A costs more than Company B, we set up the inequality: \[ 25 + 0.20b > 0.30b \]

Now, we can solve for \( b \):

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

2. Now, divide both sides by \( 0.10 \): \[ \frac{25}{0.10} > b \] \[ 250 > b \]

This means that for \( b < 250 \), Company A costs more than Company B.

To find the number of brochures for Company A to cost more than Company B, \( b \) would need to be greater than 250:

Therefore, the correct conclusion is that Company A will cost more than Company B when \( b > 250 \).