To determine the equivalent part-to-part-to-whole ratios from the given ratio of quarts of red paint to yellow paint, we can analyze the totals in the table you provided:
- The first row shows 3 quarts of red and 2 quarts of yellow, totaling 5.
- The second row shows 21 quarts of red and 14 quarts of yellow, totaling 35.
Now, let's summarize the ratios:
-
From the first row (3 red, 2 yellow):
- Part-to-part: Red : Yellow = 3 : 2
- Total = 5
-
From the second row (21 red, 14 yellow):
- Part-to-part: Red : Yellow = 21 : 14
- Total = 35
Next, we can simplify the second row's ratio:
- 21 : 14 simplifies to 3 : 2 (by dividing both by 7). So we see that the ratio of red to yellow is consistent across both rows.
Now, we want the part-to-part-to-whole ratio. Since we already have the part-to-part ratio of red to yellow (3:2), we can express it along with the total.
To express this in the format of part-to-part-to-whole:
- Red : Yellow : Total
- Red = 3, Yellow = 2, Total = 5
Thus, the part-to-part-to-whole ratio is: 3:2:5
Now, let's convert this to equivalent values for the options provided. The key is to find a multiplication that maintains the ratio.
If we scale the ratio by 5, we get:
- Red = 3 * 5 = 15
- Yellow = 2 * 5 = 10
- Total = 5 * 5 = 25
So the equivalent part-to-part-to-whole ratio would be: 15:10:25
Therefore, the correct response is: 15:10:25 (ratio of 15 to 10 to 25).
1 answer