Question
Tori bought some butterfly feeders, and she needs to fill them before she puts them in her garden. She finds a recipe online for a sugar water mixture that will attract butterflies. The recipe says to mix 1 ounce of sugar with 9 ounces of water. Tori decides to make one large batch so she can fill all her feeders at once. In a pot, she mixes 4 ounces of sugar with 36 ounces of water. Which mixture is sweeter?
Answers
GPT-4o mini
To determine which mixture is sweeter, we need to compare the sugar-to-water ratios in both mixtures.
1. **Original recipe ratio:**
- Sugar: 1 ounce
- Water: 9 ounces
- Total mixture: \(1 + 9 = 10\) ounces
- Ratio of sugar to total mixture:
\[
\frac{1 \text{ ounce}}{10 \text{ ounces}} = 0.1
\]
2. **Tori's mixture ratio:**
- Sugar: 4 ounces
- Water: 36 ounces
- Total mixture: \(4 + 36 = 40\) ounces
- Ratio of sugar to total mixture:
\[
\frac{4 \text{ ounces}}{40 \text{ ounces}} = 0.1
\]
Both mixtures have the same ratio of sugar to the total mixture, which is \(0.1\) or 10%. Thus, both mixtures are equally sweet.
1. **Original recipe ratio:**
- Sugar: 1 ounce
- Water: 9 ounces
- Total mixture: \(1 + 9 = 10\) ounces
- Ratio of sugar to total mixture:
\[
\frac{1 \text{ ounce}}{10 \text{ ounces}} = 0.1
\]
2. **Tori's mixture ratio:**
- Sugar: 4 ounces
- Water: 36 ounces
- Total mixture: \(4 + 36 = 40\) ounces
- Ratio of sugar to total mixture:
\[
\frac{4 \text{ ounces}}{40 \text{ ounces}} = 0.1
\]
Both mixtures have the same ratio of sugar to the total mixture, which is \(0.1\) or 10%. Thus, both mixtures are equally sweet.