- The ratio of grapes to blueberries is consistently \(2:1\), meaning the grapes should always be twice the amount of blueberries.
- Calculating the given options shows that only \(\frac{10}{5}\) simplifies to a ratio of \(2\).
- Therefore, the correct ratio Mandie should use is \(\boxed{\frac{10}{5}}\).
Explanation
- Analyze the Relationship between Grapes and Blueberries
We are given a table relating the amount of grapes (G) to the amount of blueberries (B) in a fruit salad. By examining the values:
(2, 1) \(\implies G/B = 2/1 = 2\)
(4, 2) \(\implies G/B = 4/2 = 2\)
(20, 10) \(\implies G/B = 20/10 = 2\)
(24, 12) \(\implies G/B = 24/12 = 2\)
In every case, the ratio of grapes to blueberries is \(2:1\), meaning \(G = 2B\). Mandie is making a fruit salad, and she must maintain this ratio of grapes to blueberries.
- Evaluate the Options and Identify the Correct Ratio
We need to identify which of the given options corresponds to a ratio of grapes to blueberries of \(2:1\). Let's calculate the value of each provided ratio:
- Option 1: \(\frac{6}{9} = \frac{2}{3} \approx 0.67\)
- Option 2: \(\frac{8}{7} \approx 1.14\)
- Option 3: \(\frac{10}{5} = 2\)
- Option 4: \(\frac{12}{3} = 4\)
The only ratio that equals 2 is \(\frac{10}{5}\). Therefore, the correct ratio of grapes to blueberries Mandie should use is \(\frac{10}{5}\).
Examples
Understanding ratios is essential for many everyday tasks, such as cooking or mixing ingredients. If a recipe for a salad dressing requires a specific ratio of oil to vinegar, you can maintain that flavor profile regardless of the total amount you prepare by keeping that ratio constant. This mathematical skill helps ensure that the quality and consistency of your preparations remain the same, whether you're making a single serving or enough for a large party.