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?

1 answer

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.