Question

If Y varies directly with X . find Y when X=15 if Y=6 when X=30

Answer 1

In a direct variation between Y and X (Y = kX), with given values Y = 6 when X = 30, the constant of variation (k) is found to be
`\((1)/(5)\)`. Substituting X = 15, we find Y = 3.

When Y varies directly with X, the relationship can be expressed as Y = kX, where k is the constant of variation.

To find k, we can use the given values when Y = 6 and X = 30:

`\[6 = k * 30\]`

Now, solve for k:

`\[k = (6)/(30) = (1)/(5)\]`

Now that we have the constant of variation k, we can use it to find Y when X = 15:

`\[Y = (1)/(5) * 15 = 3\]`

Therefore, when X = 15, Y = 3.