Question

How do you find the value of y for a given value of x, if y varies directly with x. If y=166 when x=83, what is y when x=237?

Answer 1

`474`

Explanation:

Let's write this information in a table:

`color(white)(0)x color(white)(0)|color(white)(0)ycolor(white)(0)`
....................
`color(white)(0)83 color(white)()|color(white)() 166 color(white)(0)`
`color(white)()237 color(white)()|color(white)(0) ? color(white)(0)`

Here's a pattern I noticed
`83xx2=166`

`y=2x`

Maybe the next pattern is
`237xx2=474`

Answer 2

`474`

Explanation:

`"given " ypropx`

`"to convert to an equation, multiply by k, the constant"`
`"of variation"`

`rArry=kxxx=kx`

`"to find k, use the given condition"`

`y=166" when " x=83`

`rArrk=y/x=166/83=2`

`"the equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=2x)color(white)(2/2)|)))`

`rArrx=237toy=2xx237=474`