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.