Dominic is buying supplies for his poetry class. He likes to write his poems in black ink, then decorate the pages with colorful drawings. The Mega Writer pack has 6 colored pens and 9 black pens. The Mini Writer pack has 3 colored pens and 6 black pens. Do the packs have the same ratio of colored pens to black pens?

Question

Yes or No?

Answer 1

To determine if the Mega Writer pack and the Mini Writer pack have the same ratio of colored pens to black pens, we can calculate the ratio for each pack.

Mega Writer pack:

• Colored pens: 6
• Black pens: 9

The ratio of colored pens to black pens is: \[ \text{Ratio (Mega Writer)} = \frac{\text{Colored pens}}{\text{Black pens}} = \frac{6}{9} = \frac{2}{3} \]

Mini Writer pack:

• Colored pens: 3
• Black pens: 6

The ratio of colored pens to black pens is: \[ \text{Ratio (Mini Writer)} = \frac{\text{Colored pens}}{\text{Black pens}} = \frac{3}{6} = \frac{1}{2} \]

Now we compare the two ratios:

• Mega Writer: \(\frac{2}{3}\)
• Mini Writer: \(\frac{1}{2}\)

Since \(\frac{2}{3} \neq \frac{1}{2}\), the packs do not have the same ratio of colored pens to black pens.

Answer: No