To solve for [tex]\( x \)[/tex] in the given proportion [tex]\( 12.5 \, \text{mg} : 5 \, \text{mL} = 25 \, \text{mg} : x \, \text{mL} \)[/tex], we can follow these steps:
1. Set up the proportion:
[tex]\( \frac{12.5 \, \text{mg}}{5 \, \text{mL}} = \frac{25 \, \text{mg}}{x \, \text{mL}} \)[/tex].
2. Cross multiply to eliminate the fractions:
[tex]\[ 12.5 \, \text{mg} \cdot x \, \text{mL} = 25 \, \text{mg} \cdot 5 \, \text{mL} \][/tex]
3. Simplify the right-hand side:
[tex]\[ 12.5x = 25 \times 5 \][/tex]
[tex]\[ 12.5x = 125 \][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 12.5:
[tex]\[ x = \frac{125}{12.5} \][/tex]
5. Perform the division:
[tex]\[ x = 10 \][/tex]
Therefore, [tex]\( x \)[/tex] is [tex]\( 10 \)[/tex]. This means that [tex]\( 25 \, \text{mg} \)[/tex] is equivalent to [tex]\( x \, \text{mL} \)[/tex] where [tex]\( x \)[/tex] is [tex]\( 10 \, \text{mL} \)[/tex].
