Question

3. Marjorie made 4 wreaths in 6

hours and 6 wreaths in 9 hours.
What is the constant of
proportionality?
13
k=2
k = 2/3
k = 3/2
k= 3

Answer 1

The constant of proportionality is k =
`(2)/(3)` ⇒ B

Explanation:

The form of the equation of the proportionality is y = k x, where

• k is the constant of proportionality

∵ Marjorie made 4 wreaths in 6 hours

→ Let y the number of wreath and x is the time of making them

∵ y = k x

∵ y = 4 and x = 6

→ Substitute them in the equation

∴ 4 = k(6)

∴ 4 = 6k

→ Divide both sides by 6 to find k

∵
`(4)/(6)` =
`(6k)/(6)`

∴
`(2)/(3)` = k

Let us use the other information to be sure it will give us the same value of k

∵ She made 6 wreaths in 9 hours

∴ y = 6 and x = 9

→ Substitute them in the equation

∵ 6 = k(9)

∴ 6 = 9k

→ Divide both sides by 9 to find k

∵
`(6)/(9)` =
`(9k)/(9)`

∴
`(2)/(3)` = k

∴ The constant of proportionality is k =
`(2)/(3)`