Question

If c varies directly as (r + 1) and c = 8, when r= 3, calculate the value of r when c= 20.

(4marks)​

Answer 1

r = 9

Explanation:

Given that c varies directly as (r + 1) then the equation relating them is

c = k(r + 1) ← k is the constant of variation

To find k use the condition c = 8 when r = 3, then

8 = k(3 + 1) = 4k ( divide both sides by 4 )

2 = k

c = 2(r + 1) ← equation of variation

When c = 20, then

20 = 2(r + 1) ← divide both sides by 2

10 = r + 1 ( subtract 1 from both sides )

9 = r

Answer 2

c = k(r + 1)

8 = k(3 + 1)

8 = 4k

8/4 = k

2 = k

c=2(r + 1)

When c = 20, then

20 = 2(r + 1)

20 = 2r + 2

20 - 2 = 2r

18 = 2r

18/2 = r

9 = r

Therefore, the value of r is 9 when c is 20..