Question

If y varies directly as x, and y=25 when x=5, find y when x=25

Answer 1

Answer: The required value of y is 125.

Step-by-step explanation: Given that the variable y varies directly as x. Also, y = 25 when x = 5.

We are to find the value of y when x = 25.

Given that y varies directly as x.

So, we have

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

When x = 5, y = 25, then we have

`y=kx\\\\\Rightarrow 25=k*5\\\\\Rightarrow k=(25)/(5)\\\\\Rightarrow k=5.`

So,

`y=kx\\\\\Rightarrow y=5x.`

Now, when x = 25, then the value of y will be

`y=5x=5*25=125.`

Thus, the required value of y is 125.

Answer 2

The value of y is 125 when x=25.

Explanation:

It is given that y varies directly as x. It means y is proportional to x.

`y\propto x`

`y=kx`

Where k is constant of proportionality.

It is given that y=25 when x=5. Put x=5 and y=25 in the above equation to find the value of k.

`25=k(5)`

Divide both sides by 5.

`5=k`

The value of k is 5.

The relation between x and y is defined by the equation

`y=5x`

Put x=25 in the above equation.

`y=5(25)`

`y=125`

Therefore the value of y is 125 when x=25.