Question

Lucas and his brother, Max, went to the arcade yesterday. Lucas played 2 games of Rodeo Racing and 8 games of Polar Pinball. Max played 3 games of Rodeo Racing and 9 games of Polar Pinball. Which brother played the greater ratio of Rodeo Racing to Polar Pinball?

Answer 1

To find out which brother, Lucas or Max, played a greater ratio of Rodeo Racing to Polar Pinball, we need to calculate the ratio for each brother.

**For Lucas:**
- Rodeo Racing games: 2
- Polar Pinball games: 8

The ratio of Rodeo Racing to Polar Pinball for Lucas is:
\[
\text{Ratio}_\text{Lucas} = \frac{\text{Rodeo Racing}}{\text{Polar Pinball}} = \frac{2}{8} = \frac{1}{4}
\]

**For Max:**
- Rodeo Racing games: 3
- Polar Pinball games: 9

The ratio of Rodeo Racing to Polar Pinball for Max is:
\[
\text{Ratio}_\text{Max} = \frac{\text{Rodeo Racing}}{\text{Polar Pinball}} = \frac{3}{9} = \frac{1}{3}
\]

Now, we compare the two ratios:
- Lucas: \(\frac{1}{4}\)
- Max: \(\frac{1}{3}\)

To compare these fractions, it's helpful to find a common denominator. The least common multiple of 4 and 3 is 12. We can convert both fractions:
- \(\frac{1}{4} = \frac{3}{12}\)
- \(\frac{1}{3} = \frac{4}{12}\)

Since \(\frac{3}{12} < \frac{4}{12}\), this means:
\[
\frac{1}{4} < \frac{1}{3}
\]
Thus, Max has a greater ratio of Rodeo Racing to Polar Pinball.

**Conclusion:**
Max played the greater ratio of Rodeo Racing to Polar Pinball.