Final answer:
The fewest number of vegetables that can be used to make this salad is 12.
Step-by-step explanation:
In this salad recipe, the ratio of carrots to broccoli must remain constant. Based on the table provided, we can see that for every 1 carrot, there are 3 broccoli. To determine the fewest number of vegetables that can be used, we need to find a common multiple of 3 and 9 (the smallest pair of values for carrots and broccoli).
The common multiple of 3 and 9 is 9, so we need at least 9 carrots and 27 broccoli. However, since only whole vegetables can be used, we must round up to the next whole number.
Therefore, the fewest number of vegetables that can be used to make this salad is 12.