Question

Decide whether each table could represent a proportional relationship. If the

relationship could be proportional, what would be the constant of proportionality?

Answer 1

Explanation:

If given tables in the picture show the proportional relationship,

Number of wheels (w) ∝ Number of buses (b)

w ∝ b

w = kb

Here, k = proportionality constant

k =
`(w)/(b)`

Number of buses (b) Number wheels (w) Wheels per bus
`((w)/(b))`

5 30
`(30)/(5)=6`

8 48
`(48)/(8)=6`

10 60
`(60)/(10)=6`

15 90
`(90)/(15)=6`

Here, proportionality constant is 6.

Similarly, If number of wheels (w) ∝ Number of train cars (t)

w = kt

Here, k = proportionality constant

k =
`(w)/(t)`

Number of train cars(t) Number of wheels(w) Wheels per train car (
`(w)/(t)`)

20 184
`(184)/(20)=9.2`

30 264
`(264)/(30)=8.8`

40 344
`(344)/(40)=8.6`

50 424
`(424)/(50)=8.48`

Since, ratio of w and t is not constant, relation between number of wheels and number of train cars is not proportional.