Volunteer drivers are needed to bring 80 students to the championship baseball game. Drivers either have cars, which can seat 4 students, or vans, which can seat 6 students. The equation LaTeX: 4c+6v=804 c + 6 v = 80 describes the relationship between the number of cars, LaTeX: cc, and number of vans, LaTeX: vv, that can transport exactly 80 students. Select all statements that are true about the situation. Group of answer choices A. If 2 cars go, then 2 vans are needed.

B. LaTeX: c=14 c = 14 and LaTeX: v=4 v = 4 are a pair of solutions to the equation.

C. If 6 cars go and 11 vans go, there will be extra space

D. 10 cars and 8 vans isn't enough to transport all the students.

E. If 20 cars go, no vans are needed.

F. 8 vans and 8 cars are numbers that meet the constraints in this situation.

B. c =14 v = 4 are a pair of solutions to the equation.

E. If 20 cars go, no vans are needed.

F. 8 vans and 8 cars are numbers that meet the constraints in this situation.

Step-by-step explanation:

Volunteer drivers are needed to bring 80 students to the championship baseball game. Drivers either have cars, which can seat 4 students, or vans, which can seat 6 students. The equation

4 c + 6 v = 80

We are to find what can transport exactly 80 students.

We compare the options till we get our correct answer.

A. If 2 cars go, then 2 vans are needed.

4 c + 6 v = 80

c = number of cars needed

v = number of vans needed

Hence,

4(2) + 6(2)

8 + 12 ≠ 80

20≠ 80

Option A is wrong

B. c =14 v = 4 are a pair of solutions to the equation.

4 c + 6 v = 80

c = number of cars needed

v = number of vans needed

Hence,

4(14) + 6(4) = 80

56 + 24 = 80

80 = 80

Option B is correct

C. If 6 cars go and 11 vans go, there will be extra space

4 c + 6 v = 80

c = number of cars needed

v = number of vans needed

Hence,

4(6) + 6(11)

24 + 66

110 > 80

Option C is wrong, there would be no space left

D. 10 cars and 8 vans isn't enough to transport all the students.

4 c + 6 v = 80

c = number of cars needed

v = number of vans needed

Hence,

4(10) + 6(8)

40 + 48

88 > 80

Option D is wrong

E. If 20 cars go, no vans are needed.

4 c + 6 v = 80

c = number of cars needed

v = number of vans needed

Hence,

4(20) + 6(0) = 80

80 + 0 = 80

80 = 80

Option E is correct

F. 8 vans and 8 cars are numbers that meet the constraints in this situation.

4 c + 6 v = 80

c = number of cars needed

v = number of vans needed

Hence,

4(8) + 6(8) = 80

32 + 48 = 80

80 = 80

Option F is correct

Therefore the statements in options B, E and F are the only correct statement for the equation 4 c + 6 v = 80

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