Answer:
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.
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