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?

Answer 1

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

The total cost for Company A can be expressed as:
\[
\text{Cost}_A = 25 + 0.20x
\]

The total cost for Company B can be expressed as:
\[
\text{Cost}_B = 0.30x
\]

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

Now, we can solve the inequality. First, subtract \( 0.20x \) from both sides:
\[
25 > 0.30x - 0.20x
\]

This simplifies to:
\[
25 > 0.10x
\]

Next, to isolate \( x \), divide both sides by 0.10:
\[
x < \frac{25}{0.10}
\]
\[
x < 250
\]

Thus, Company A costs more than Company B when the number of brochures ordered is less than 250.

To find the number of brochures for which Company A costs more than Company B, we can also check at \( x = 250 \):
At \( x = 250 \):
- Cost of Company A:
\[
\text{Cost}_A = 25 + 0.20(250) = 25 + 50 = 75
\]
- Cost of Company B:
\[
\text{Cost}_B = 0.30(250) = 75
\]

At \( x = 250 \), both costs are equal. Therefore, Company A starts to be more costly than Company B for \( x = 251 \) or more.

In conclusion, Company A costs more than Company B when the number of brochures ordered is:

\[
\boxed{251}
\] or more.