Choose the inequality that matches this situation.

Question

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?
$0.20b + $0.30b > 25b
$0.20b+ $0.30b <25b
$25+ $0.20b > $0.30b
$25+ $0.20b < $0.30b

Answer 1

To determine when Company A costs more than Company B, let's define the variables and set up the inequalities based on their pricing structures.

Let \( b \) be the number of brochures ordered.

• Company A's cost: \( 25 + 0.20b \)
• Company B's cost: \( 0.30b \)

We want to find when Company A's cost is greater than Company B's cost:

\[ 25 + 0.20b > 0.30b \]

Now let's rearrange this inequality:

1. Subtract \( 0.20b \) from both sides:

\[ 25 > 0.30b - 0.20b \]

2. This simplifies to:

\[ 25 > 0.10b \]

3. Finally, dividing both sides by \( 0.10 \):

\[ 250 > b \]

This means Company A will cost more than Company B if fewer than 250 brochures are ordered.

From the answer choices provided, the correct inequality is:

\[ 25 + 0.20b > 0.30b \]

This is the inequality that matches the situation.