Question

Shawn and Robert are comparing the scout patches they've earned. Shawn has a total of 8 patches, 5 of which are explorer patches. Robert has a total of 6 patches, 3 of which are explorer patches. Do Shawn and Robert have the same ratio of explorer patches to total patches?

Answer 1

To determine if Shawn and Robert have the same ratio of explorer patches to total patches, we can calculate the ratio for each of them.

For Shawn:
- Total patches = 8
- Explorer patches = 5

The ratio of explorer patches to total patches for Shawn is:
\[
\text{Ratio for Shawn} = \frac{\text{Explorer Patches}}{\text{Total Patches}} = \frac{5}{8}
\]

For Robert:
- Total patches = 6
- Explorer patches = 3

The ratio of explorer patches to total patches for Robert is:
\[
\text{Ratio for Robert} = \frac{\text{Explorer Patches}}{\text{Total Patches}} = \frac{3}{6} = \frac{1}{2}
\]

Now we compare the two ratios:
- Shawn's ratio is \(\frac{5}{8}\)
- Robert's ratio is \(\frac{1}{2}\)

To compare these ratios, we can find a common denominator:

Converting \( \frac{1}{2} \) to have the same denominator as \( \frac{5}{8} \):
\[
\frac{1}{2} = \frac{4}{8}
\]

Now we see:
- Shawn: \( \frac{5}{8} \)
- Robert: \( \frac{4}{8} \)

Since \( \frac{5}{8} \) is different from \( \frac{4}{8} \), Shawn and Robert do **not** have the same ratio of explorer patches to total patches.