Question

Last night, Clara and her brother, Stefan, made personal pizzas for dinner. Clara put 4 pepperoni pieces and 6 ham pieces on her pizza. Stefan put 6 pepperoni pieces and 10 ham pieces on his pizza. Did Clara's and Stefan's pizzas have the same ratio of pepperoni pieces to ham pieces?

Answer 1

To determine if Clara's and Stefan's pizzas had the same ratio of pepperoni pieces to ham pieces, we can calculate the ratio for each pizza.

**Clara's Pizza:**
- Pepperoni pieces: 4
- Ham pieces: 6

The ratio of pepperoni to ham for Clara is:
\[
\text{Clara's ratio} = \frac{4 \text{ pepperoni}}{6 \text{ ham}} = \frac{4}{6} = \frac{2}{3}
\]

**Stefan's Pizza:**
- Pepperoni pieces: 6
- Ham pieces: 10

The ratio of pepperoni to ham for Stefan is:
\[
\text{Stefan's ratio} = \frac{6 \text{ pepperoni}}{10 \text{ ham}} = \frac{6}{10} = \frac{3}{5}
\]

Now we compare the two ratios:
- Clara's ratio is \( \frac{2}{3} \)
- Stefan's ratio is \( \frac{3}{5} \)

To compare \( \frac{2}{3} \) and \( \frac{3}{5} \), we can find a common denominator, which is 15.

Convert Clara's ratio:
\[
\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}
\]

Convert Stefan's ratio:
\[
\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}
\]

Now we can compare:
- Clara's ratio: \( \frac{10}{15} \)
- Stefan's ratio: \( \frac{9}{15} \)

Since \( \frac{10}{15} \neq \frac{9}{15} \), Clara's and Stefan's pizzas do not have the same ratio of pepperoni pieces to ham pieces.

In conclusion, **Clara's and Stefan's pizzas do not have the same ratio of pepperoni pieces to ham pieces.**