Question

If y is 5 when x is 2.5 and y varies directly with x, find y when x is 10

Answer 1

Answer: The required value of y is 20.

Step-by-step explanation: Given that y is 5 when x is 2.5 and y varies directly with x.

We are to find the value of y when x is 10.

According to the given information, we can write

`y\propto x\\\\\Rightarrow y=kx~~~~~~~~~~[\textup{where k is the constant of proportionality}]`

When y = 5 and x = 2.5, then we have

`5=k*2.5\\\\\Rightarrow k=(5)/(2.5)\\\\\Rightarrow k=2.`

So, we get

`y=2x.`

Therefore, when x = 10, then the value of y is

`y=2*10=20.`

Thus, the required value of y is 20.

Answer 2

If x varies directly as y, then x=ky. y=5 and x=2.5 are substituted into x=ky to find k.

2.5=5k

k=2.5/5

k=5.

K =5 is substituted in x=ky to find y where x is 10.

x=5y

10=5y

y=10/2

y=2