Question

Answer the question correctly for good luck

If ‘c’ is directly proportional to‘d’ and c = 24 when d = 4

Find an equation connecting ‘c’ and ‘d’

Find ‘c’ when d = 8

Find ‘d’ when c = 54

Answer 1

• The equation connecting c and d is: c = kd
• The value of c when d=8 is: 48
• The value of d when c=54 is: 9

Explanation:

Proportion can be defined as the effect of changing one quantity on the other.

Given that

‘c’ is directly proportional to‘d’

It can mathematically be written as:

c∝d

A constant is introduced in the equation when the proportionality symbol will be removed. The constant is called constant of proportionality

`c =kd`

Given that

c = 24 when d = 4

Putting the values

`24 = k(4)\\k = (24)/(4)\\k = 6`

Putting the value of k

`c = 6d`

Putting d = 8

`c = 6(8) = 48`

Putting c = 54

`54 = 6d\\d = (54)/(6)\\d = 9`

Hence,

• The equation connecting c and d is: c = kd
• The value of c when d=8 is: 48
• The value of d when c=54 is: 9