To determine whether the Mega Writer pack and the Mini Writer pack have the same ratio of colored pens to black pens, we need to calculate the ratios for each pack.
For the Mega Writer pack:
- Colored pens: 6
- Black pens: 9
The ratio of colored pens to black pens in the Mega Writer pack is: \[ \text{Ratio (Mega Writer)} = \frac{6 \text{ colored pens}}{9 \text{ black pens}} = \frac{6}{9} = \frac{2}{3} \]
For the Mini Writer pack:
- Colored pens: 3
- Black pens: 6
The ratio of colored pens to black pens in the Mini Writer pack is: \[ \text{Ratio (Mini Writer)} = \frac{3 \text{ colored pens}}{6 \text{ black pens}} = \frac{3}{6} = \frac{1}{2} \]
Comparing the ratios:
- Mega Writer pack ratio: \( \frac{2}{3} \)
- Mini Writer pack ratio: \( \frac{1}{2} \)
To compare these ratios, we can find a common denominator:
- The common denominator for 3 and 2 is 6.
Converting the ratios:
- \( \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \)
- \( \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \)
Now we can compare:
- Mega Writer: \( \frac{4}{6} \)
- Mini Writer: \( \frac{3}{6} \)
Since \( \frac{4}{6} \) is not equal to \( \frac{3}{6} \), the two packs do not have the same ratio of colored pens to black pens.
Thus, the answer is No, the packs do not have the same ratio of colored pens to black pens.