Choose the inequality that matches this situation.

Question

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

answers:

$0.20b + $0.30b > 25b

$0.20b + $0.30 < 25b

$25 + $0.20b > $0.30b

$25 + $0.20b < $0.30b

Answer 1

To determine at what point Company A would cost more than Company B, we can set up the equation based on their pricing structures.

• Company A: Charges $25 plus $0.20 per brochure. The cost can be expressed as: \[ \text{Cost A} = 25 + 0.20b \]

• Company B: Charges $0.30 per brochure. The cost can be expressed as: \[ \text{Cost B} = 0.30b \]

We want to find the number of brochures \( b \) for which Company A's cost is greater than Company B's cost: \[ 25 + 0.20b > 0.30b \]

This inequality corresponds to the option: \[ $25 + $0.20b > $0.30b \]

So, the correct answer is: $25 + $0.20b > $0.30b.

Answer 2

are you sure

Answer 3

Yes, let's double-check the reasoning step-by-step:

1. Cost for Company A:

   • Base fee: $25
   • Cost per brochure: $0.20
   • Total cost for \( b \) brochures: \( 25 + 0.20b \)

2. Cost for Company B:

   • Cost per brochure: $0.30
   • Total cost for \( b \) brochures: \( 0.30b \)

3. Finding when Company A costs more than Company B:

   • We need to set up the inequality: \[ 25 + 0.20b > 0.30b \]

This means that the expression indicating when Company A's total cost exceeds Company B's total cost is indeed: \[ 25 + 0.20b > 0.30b \]

Thus, my initial statement about the inequality matching the situation in your question is correct. The answer is: $25 + $0.20b > $0.30b.