Question

Determine the constant of variation for the direct variation given.

Fat calories varies directly with the grams of fat. There are 27 calories for each 3 grams of fat.
1/9
3
9

Answer 1

`If\ fat\ calories\ varies\ directly\ as\ grams\ of\ fat\ we\ have\ ratio:\\\\(27)/(3)=k,\ \ where\ k-constant\ variation\\\\ k=9`

Answer 2

9

Explanation:

Direct Variation problems always take the form
`A=kB`

Where,

A is one variable and B is another one.

`k` is the proportionality constant or constant of variation.

In this problem we are talking about fat calories and grams of fat. We can assign any variable to them.

Let's denote fat calories as C and grams of fat as G.

So from the direct variation general form given above, we can write:

`C=kG`

Given that
`C=27` and
`G=3`, we can substitute these values into the equation and solve for
`k`.

`C=kG\\(27)=k(3)\\k=(27)/(3)=9`

So the constant of variation is 9.