Question

Choose the inequality that matches this situation.

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

are you sure

Answer 2

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 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**.