1) To solve the first proportion, we first convert mixed numbers to improper fractions:
8 1/8 = 65/8
2 1/2 = 5/2

Now we have:
65/8 : 5/2 = 2 2/3 : x

Next we invert the second ratio:
65/8 2/5 = 2 2/3 x

Multiplying the fractions:
(65 2) / (8 5) = (8/3) * x
130 / 40 = 8x/3
13/4 = 8x/3

Cross multiply to solve for x:
3 13 = 8x 4
39 = 32x
x = 39/32

Therefore, the value of x is 39/32.

2) To solve the second proportion, we have:
24 : 36 = x : 4

Cross multiply:
24 4 = 36 x
96 = 36x
x = 96 / 36
x = 2.67

So, the value of x is 2.67.

3) To solve the third proportion:
x : 9 = 15 : 24

Cross multiply:
x 24 = 9 15
24x = 135
x = 135 / 24
x = 5.625

Therefore, the value of x is 5.625.