volunteer drivers are needed to bring 80 students to the championship baseball game. drivers either have…

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 4c + 6v = 80 describes the relationship between the number of cars, c, and number of vans, v, that can transport exactly 80 students. select all statements that are true about the situation. a if 12 cars go, then 2 vans are needed. b the pair c = 14 and v = 4 is a solution to the equation. c if 6 cars go and 11 vans go, there will be extra space. d 10 cars and 8 vans isnt 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.

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 4c + 6v = 80 describes the relationship between the number of cars, c, and number of vans, v, that can transport exactly 80 students. select all statements that are true about the situation. a if 12 cars go, then 2 vans are needed. b the pair c = 14 and v = 4 is a solution to the equation. c if 6 cars go and 11 vans go, there will be extra space. d 10 cars and 8 vans isnt 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.

Answer

Explanation:

Step1: Analyze the equation

The equation is (4c + 6v=80), where (c) is the number of cars and (v) is the number of vans.

Step2: Check option A

If (c = 12), then (4\times12+6v=80), (48 + 6v=80), (6v=80 - 48=32), (v=\frac{32}{6}=\frac{16}{3}\notin\mathbb{Z}), so 2 vans are not enough when (c = 12), option A is false.

Step3: Check option B

Substitute (c = 14) and (v = 4) into the equation (4c+6v). We get (4\times14+6\times4=56 + 24=80), so ((c = 14,v = 4)) is a solution, option B is true.

Step4: Check option C

If (c = 6) and (v = 11), then (4\times6+6\times11=24+66 = 90>80), there will be extra - space, option C is true.

Step5: Check option D

If (c = 10) and (v = 8), then (4\times10+6\times8=40 + 48=88>80), 10 cars and 8 vans are more than enough to transport 80 students, option D is true.

Step6: Check option E

If (c = 20), then (4\times20=80), so no vans are needed when (c = 20), option E is true.

Step7: Check option F

Substitute (c = 8) and (v = 8) into (4c + 6v), we have (4\times8+6\times8=32+48 = 80), so 8 vans and 8 cars are numbers that meet the constraints, option F is true.

Answer:

B. The pair (c = 14) and (v = 4) is a solution 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.