Answer:

find the value of k when y varies directly as x, we can use the formula y = kx, where k is the constant of proportionality. This formula tells us that the value of y is equal to the value of k multiplied by the value of x.

Using this formula, we can find the value of k for each of the given relationships:

1. y = 24 when x = 3: 24 = k * 3, so k = 24/3 = 8

2. y = 4 when x = 5⅓: 4 = k * (5⅓), so k = 4 / (5⅓) = 8/5

3. x = 15 when y = 120: 120 = 15k, so k = 120/15 = 8

4. x = 42 when y = 96: 96 = 42k, so k = 96/42 = 8/2 = 4

5. x = 42 when y = 14: 14 = 42k, so k = 14/42 = 1/3

6. x = 9 when y = 21: 21 = 9k, so k = 21/9 = 7/3

So, the value of k varies depending on the given relationship.