Question

3. 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 40 + 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. c = 14 and 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.

Answer 1

Options (B), (C) and (E) are the correct options.

Explanation:

Equation that represents relation between the number of cars c and the number of vans v to transport 80 students is,

4c + 6v = 80

Option A.

If c = 12,

4(12) + 6(v) = 80

48 + 6v = 80

6v = 32

`v=(16)/(3)`

Which is not equal to 2.

Therefore, Option A is incorrect.

Option B

If c = 14,

4(14) + 6(v) = 80

56 + 6v = 80

6v = 24

v = 4

Therefore, c = 14 and v = 4 is a pair of solutions.

Option B is correct.

Option C.

If c = 6 and v = 11

4(6) + 6(11) = 24 + 66

= 90

This means with 6 cars and 11 vans 90 students can be transported. Therefore, there will be extra space.

Option C is correct.

Option D.

If c = 10 and v = 8

4(10) + 6(8) = 40 + 48

= 88

Therefore, 10 cars and 8 vans are enough to transport 80 students.

So option D is incorrect.

Option E.

If c = 20,

4(20) + 6(v) = 80

80 + 6v = 80

v = 0

Therefore, for 20 cars go no vans are needed.

Option E is correct.

Option F.

Constraints in this situation,

Minimum number of cars to be used = 20

c ≥ 20

Minimum number of vans to be used =
`(80)/(6)` ≈ 14

v ≥ 14

Therefore, Option (F) is incorrect.