Question

1) If a varies directly to b and a= 28 when b= -4, find a when b= -8 2) If x varies directly to w and x = 5 when w= 15, what is x when w = 27?​

Answer 1

(1) a = 56 , (2) x = 9

Explanation:

(1)

given a varies directly to b , then the equation relating them is

a = kb ← k is the constant of variation

to find k, substitute a = 28, b = - 4 into the equation

28 = - 4k ( divide both sides by - 4 )

- 7 = k

a = - 7b ← equation of variation

when b = - 8 , then

a = - 7 × - 8 = 56

(2)

given x varies directly to w , then the equation relating them is

x = kw ← k is the constant of variation

to find k , substitute x = 5, w = 15 into the equation

5 = 15k ( divide both sides by 15 )

`(5)/(15)` = k , that is

k =
`(1)/(3)`

x =
`(1)/(3)` w ← equation of variation

when w = 27 , then

x =
`(1)/(3)` × 27 = 9