If a:b=5:8, x:y=25:16, evaluate a/x

From $a:b = 5:8$, we have:

$$\frac{a}{b} = \frac{5}{8}$$

From $x:y = 25:16$, we have:

$$\frac{x}{y} = \frac{25}{16}$$

From $\frac{a}{b} = \frac{5}{8}$, we can write $a$:

$$a = \frac{5}{8}b$$

From $\frac{x}{y} = \frac{25}{16}$, we can write $x$:

$$x = \frac{25}{16}y$$

To simplify, multiply the numerator by the reciprocal of the denominator:

$$\frac{a}{x} = \frac{5}{8}b \times \frac{16}{25y}$$ $$\frac{a}{x} = \frac{5 \times 16 \times b}{8 \times 25 \times y}$$

Now, simplify the numerical part:

$$\frac{a}{x} = \frac{80b}{200y}$$

Divide both the numerator and the denominator of the numerical fraction by their greatest common divisor, which is 40:

$$\frac{a}{x} = \frac{80 \div 40}{200 \div 40} \cdot \frac{b}{y}$$ $$\frac{a}{x} = \frac{2}{5} \cdot \frac{b}{y}$$

The expression for $\frac{a}{x}$ is:

$$\frac{2b}{5y}$$