Question
Making a certain shade of paint requires mixing 3 parts silver with 4 parts green. Meg uses this data to start this table of equivalent ratios.
Which ratios are equivalent to 3 parts silver paint to 4 parts green paint? Check the two that apply.
(2 points)
Responses
5:6
5:6
9:12
9:12
6:8
6:8
4:5
Which ratios are equivalent to 3 parts silver paint to 4 parts green paint? Check the two that apply.
(2 points)
Responses
5:6
5:6
9:12
9:12
6:8
6:8
4:5
Answers
GPT-4o mini
To determine which ratios are equivalent to the ratio of 3 parts silver to 4 parts green (which can be expressed as 3:4), we can simplify the ratios given in the responses to see if they match.
1. **5:6** - This simplifies to 5 parts silver and 6 parts green. To compare, we can cross-multiply: \(5 \times 4 \neq 6 \times 3\). Therefore, this ratio is not equivalent.
2. **9:12** - This ratio can be simplified by dividing both parts by 3, resulting in 3:4. So, this ratio is equivalent.
3. **6:8** - This ratio can be simplified by dividing both parts by 2, resulting in 3:4. So, this ratio is also equivalent.
4. **4:5** - Cross-multiplying gives \(4 \times 4 \neq 5 \times 3\), so this ratio is not equivalent.
**Correct answers**: **9:12** and **6:8**.
1. **5:6** - This simplifies to 5 parts silver and 6 parts green. To compare, we can cross-multiply: \(5 \times 4 \neq 6 \times 3\). Therefore, this ratio is not equivalent.
2. **9:12** - This ratio can be simplified by dividing both parts by 3, resulting in 3:4. So, this ratio is equivalent.
3. **6:8** - This ratio can be simplified by dividing both parts by 2, resulting in 3:4. So, this ratio is also equivalent.
4. **4:5** - Cross-multiplying gives \(4 \times 4 \neq 5 \times 3\), so this ratio is not equivalent.
**Correct answers**: **9:12** and **6:8**.