Question

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. *

Answer 1

Answer: The answer is B,E,and F

Step-by-step explanation:

Answer 2

$4c + 6v = 80$ is an illustration of a linear representation of equations

The true statements are:

• (b) 14 cars require 4 vans
• (e) No vans are needed If there are 20 cars
• (f) 8 cars require 8 vans

First, we analyze the options

(a) 2 cars will require 2 vans

This means that:

$(c,v) = (2,2)$

Substitute these values in $4c + 6v = 80$

$4 \times 2 + 6 \times 2 = 80$

$8 + 12 = 80$

$20= 80$

The above is not true

i.e. $20 \ne 80$

Hence, (a) is false

(b) c = 14 and v = 4

Substitute 14 for c and 4 for v

$4c + 6v = 80$

$4 \times 14 + 6 \times 4 = 80$

$56 + 24 = 80$

$80= 80$

Option (b) is true

(c) There will be extra space when 6 cars and 11 vans go

Substitute 6 for c and 11 for v

$4c + 6v = 80$

$4 \times 6 + 6 \times 11 = 80$

$24+ 66 = 80$

$90 = 80$

Option (c) is wrong because the result of the inequality should be less than 80

(d) 10 cars and 8 vans is not enough

Substitute 10 for c and 8 for v

$4c + 6v = 80$

$4 \times 10 + 6 \times 8 = 80$

$40 + 48 = 80$

$88 = 80$

(d) is false, because the result should be less than 80

(e) If 20 cars go, then no vans are needed

This means that:

c = 20, v = 0

So, we have:

$4c + 6v = 80$

$4 \times 20 + 6 \times 0 = 80$

$80 + 0 = 80$

$80 = 80$

Option (e) is true

(f) 8 cars and 8 vans would satisfy the equation

This means that:

c = 8, v = 8

So, we have:

$4c + 6v = 80$

$4 \times 8 + 6 \times 8 = 80$

$32 + 48 = 80$

$80= 80$

Option (f) is true

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