We need to solve for the unknowns $y$, $t$, $w$, and $m$ in the given proportion problems.

1. Problem Description

We need to solve for the unknowns $y$, $t$, $w$, and $m$ in the given proportion problems.

2. Solution Steps

a. We are given $10:y = 2:3$. This can be written as a fraction:

$\frac{10}{y} = \frac{2}{3}$

Cross-multiplying, we get:

$2y = 10 \times 3$

$2y = 30$

$y = \frac{30}{2}$

$y = 15$

b. We are given $20:25 = t:5$. This can be written as a fraction:

$\frac{20}{25} = \frac{t}{5}$

Cross-multiplying, we get:

$25t = 20 \times 5$

$25t = 100$

$t = \frac{100}{25}$

$t = 4$

c. We are given $y:15 = 9:45$. This can be written as a fraction:

$\frac{y}{15} = \frac{9}{45}$

Cross-multiplying, we get:

$45y = 15 \times 9$

$45y = 135$

$y = \frac{135}{45}$

$y = 3$

d. We are given $2:w = 10:5$. This can be written as a fraction:

$\frac{2}{w} = \frac{10}{5}$

Cross-multiplying, we get:

$10w = 2 \times 5$

$10w = 10$

$w = \frac{10}{10}$

$w = 1$

e. We are given $72:27 = 8:m$. This can be written as a fraction:

$\frac{72}{27} = \frac{8}{m}$

Cross-multiplying, we get:

$72m = 27 \times 8$

$72m = 216$

$m = \frac{216}{72}$

$m = 3$

3. Final Answer

a. $y = 15$

b. $t = 4$

c. $y = 3$

d. $w = 1$

e. $m = 3$