Question

Given that y and x are directly proportional and

- y=5 when x=2, find the value of x when y=15.


- y=22 when x=6, find the value of y when x=15.


Please explain.

Answer 1

Part 1 : The value of x is 6.

Part 2 : The value of y is 55.

Explanation:

Given,

y and x are directly proportional,

i.e. y ∝ x

⇒ y = kx -----(1)

Where,

k = constant of proportionality,

Part 1 : We have,

y = 5 when x = 2,

From equation (1),

5 = 2k ⇒ k = 2.5

Thus, the equation that shows the relation between x and y is,

`y= 2.5x`

if y = 15,

`15 = 2.5x\implies x = (15)/(2.5)=6`

Hence, the value of x is 6.

Part 2 : we have,

y = 22 when x = 6,

From equation (1),

22 = 6k ⇒
`k = (22)/(6)`,

Thus, the equation that shows the relation between x and y is,

`y = (22)/(6)x`

if x = 15,

`y = (22)/(6)* 15=(11)/(3)* 15 = 11* 5 = 55`

Hence, the value of y would be 55.