A group of students was surveyed about their favorite vegetable. Green beans were chosen by 0.35 of the students, broccoli was chosen by 0.2 of the students, peas were chosen by 14

To determine which vegetable was chosen by the greatest number of students, we need to express all the choices in terms of the total number of students surveyed. Let's denote the total number of students as \( N \).

1. Green beans: Chosen by 0.35 of the students.

   • Number of students choosing green beans = \( 0.35N \)

2. Broccoli: Chosen by 0.2 of the students.

   • Number of students choosing broccoli = \( 0.2N \)

3. Peas: Given that 14 students chose peas.

   • Number of students choosing peas = 14

4. Corn: Chosen by 20% of the students.

   • Number of students choosing corn = \( 0.2N \)

Now we can compare the choices relative to each other by substituting a value for \( N \). We know peas are chosen by 14 students, so we can find \( N \) if we denote it using one of the other percentages.

To make a comparison straightforward, assume \( N = 100 \) (which allows easy calculation with percentages):

• Green beans: \( 0.35N = 0.35 \times 100 = 35 \)
• Broccoli: \( 0.2N = 0.2 \times 100 = 20 \)
• Peas: \( 14 \)
• Corn: \( 0.2N = 0.2 \times 100 = 20 \)

Now we compare the quantities:

• Green beans: 35 students
• Broccoli: 20 students
• Peas: 14 students
• Corn: 20 students

The vegetable chosen by the greatest number of students is green beans (35 students).

Thus, the answer is 1 (for green beans).