Scarlett is buying treats from a candy shop to share with her friends from Science Club. There's a Buggy Bundle box with 8 butterfly gummies and 10 beetle gummies, and a Classic Critter box with 6 butterfly gummies and 8 beetle gummies. Do the boxes have the same ratio of butterfly gummies to beetle gummies?

Answer 1

To determine whether the Buggy Bundle box and the Classic Critter box have the same ratio of butterfly gummies to beetle gummies, we need to calculate the ratio for each box.

1. Buggy Bundle box:

   • Butterfly gummies: 8
   • Beetle gummies: 10

   The ratio of butterfly gummies to beetle gummies in the Buggy Bundle box is: \[ \text{Ratio} = \frac{\text{Butterfly gummies}}{\text{Beetle gummies}} = \frac{8}{10} = \frac{4}{5} \text{ (simplified)} \]

2. Classic Critter box:

   • Butterfly gummies: 6
   • Beetle gummies: 8

   The ratio of butterfly gummies to beetle gummies in the Classic Critter box is: \[ \text{Ratio} = \frac{\text{Butterfly gummies}}{\text{Beetle gummies}} = \frac{6}{8} = \frac{3}{4} \text{ (simplified)} \]

Now we compare the two ratios:

• Buggy Bundle: \( \frac{4}{5} \)
• Classic Critter: \( \frac{3}{4} \)

To compare these fractions, we can find a common denominator. The least common multiple of 5 and 4 is 20.

• Convert \( \frac{4}{5} \) to have a denominator of 20: \[ \frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20} \]

• Convert \( \frac{3}{4} \) to have a denominator of 20: \[ \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20} \]

Now we see that: \[ \frac{16}{20} \neq \frac{15}{20} \]

This shows that the ratios \( \frac{4}{5} \) and \( \frac{3}{4} \) are not equal.

Therefore, the boxes do not have the same ratio of butterfly gummies to beetle gummies.