Question

Suppose that y varies directly with x, and y=15 when x=24. Write a direct variation equation that relates x and y. Find y when x=3

Answer 1

Just set up a proportion with the original numbers and then the numbers you want to find like so: (x1/y1)=(x2/y2) and since you want to find the second y value, just leave y as a variable like so: (15/24)=(3/y) after this just cross multiply and get the answer: 15y=72.....y=4.8

Answer 2

`y=(5)/(8)x`

`y=(15)/(8)`, when
`x=3`.

Explanation:

We have been given that y varies directly with x, and
`y=15` when
`x=24`.

We know that two direct proportional quantities are in form
`y=kx`, where k is constant of proportionality.

Let us find constant of proportionality by substituting
`y=15` and
`x=24` in above equation.

`15=k*24`

`(15)/(24)=(k*24)/(24)`

`(3*5)/(3*8)=k`

`(5)/(8)=k`

Therefore, our required equation would be
`y=(5)/(8)x`.

Let us substitute
`x=3` in the equation.

`y=(5)/(8)(3)`

`y=(15)/(8)`

Therefore, the value of y is
`(15)/(8)`.