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

Answer:

Part 1 : The value of x is 6.

Part 2 : The value of y is 55.

Step-by-step 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,

$15 = 2.5x\implies x = \frac{15}{2.5}=6$

Hence, the value of x is 6.

Part 2 : we have,

y = 22 when x = 6,

From equation (1),

22 = 6k ⇒ $k = \frac{22}{6}$,

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

$y = \frac{22}{6}x$

if x = 15,

$y = \frac{22}{6}\times 15=\frac{11}{3}\times 15 = 11\times 5 = 55$

Hence, the value of y would be 55.