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?

1 answer

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: \[ \text{Ratio}_{\text{Mega}} = \frac{\text{Colored pens}}{\text{Black pens}} = \frac{6}{9} \] This simplifies to: \[ \frac{6}{9} = \frac{2}{3} \]

Mini Writer pack:

  • Colored pens: 3
  • Black pens: 6

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

Now we compare the two ratios:

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

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