Question
Sugar Rounds Donut Shop offers 2 free donuts with every 20 purchased donuts. Sweet Delights Donut Shop offers 3 free donuts with every 30 purchased donuts. Which donut shop offers a greater ratio of free donuts to purchased donuts?
Answers
GPT-4o mini
To compare the ratio of free donuts to purchased donuts at both shops, we can calculate the ratio for each shop.
**Sugar Rounds Donut Shop:**
- For every 20 purchased donuts, they offer 2 free donuts.
- The total number of donuts (purchased + free) is \(20 + 2 = 22\).
- The ratio of free donuts to purchased donuts is:
\[
\text{Ratio} = \frac{\text{Free donuts}}{\text{Purchased donuts}} = \frac{2}{20} = \frac{1}{10} = 0.1 \quad \text{(or 10%)}
\]
**Sweet Delights Donut Shop:**
- For every 30 purchased donuts, they offer 3 free donuts.
- The total number of donuts (purchased + free) is \(30 + 3 = 33\).
- The ratio of free donuts to purchased donuts is:
\[
\text{Ratio} = \frac{\text{Free donuts}}{\text{Purchased donuts}} = \frac{3}{30} = \frac{1}{10} = 0.1 \quad \text{(or 10%)}
\]
**Comparison:**
Both donut shops offer the same ratio of free donuts to purchased donuts, which is \(0.1\) or \(10\%\). Therefore, neither shop offers a greater ratio; they both offer the same ratio of free donuts to purchased donuts.
**Sugar Rounds Donut Shop:**
- For every 20 purchased donuts, they offer 2 free donuts.
- The total number of donuts (purchased + free) is \(20 + 2 = 22\).
- The ratio of free donuts to purchased donuts is:
\[
\text{Ratio} = \frac{\text{Free donuts}}{\text{Purchased donuts}} = \frac{2}{20} = \frac{1}{10} = 0.1 \quad \text{(or 10%)}
\]
**Sweet Delights Donut Shop:**
- For every 30 purchased donuts, they offer 3 free donuts.
- The total number of donuts (purchased + free) is \(30 + 3 = 33\).
- The ratio of free donuts to purchased donuts is:
\[
\text{Ratio} = \frac{\text{Free donuts}}{\text{Purchased donuts}} = \frac{3}{30} = \frac{1}{10} = 0.1 \quad \text{(or 10%)}
\]
**Comparison:**
Both donut shops offer the same ratio of free donuts to purchased donuts, which is \(0.1\) or \(10\%\). Therefore, neither shop offers a greater ratio; they both offer the same ratio of free donuts to purchased donuts.