Sure, let's solve this step by step.
1. Understand the ratio given: The ratio of two numbers is 2:5. This means that for every 2 parts of the smaller number, there are 5 parts of the bigger number.
2. Identify the known values: We know the bigger number is 30.
3. Set up the ratio equation: Since the ratio is 2:5, we can write this as:
[tex]\[
\frac{\text{smaller number}}{\text{bigger number}} = \frac{2}{5}
\][/tex]
4. Express the smaller number using the ratio and the given bigger number: We can rearrange the ratio equation to solve for the smaller number. Let [tex]\( S \)[/tex] be the smaller number and [tex]\( B \)[/tex] be the bigger number.
[tex]\[
\frac{S}{30} = \frac{2}{5}
\][/tex]
5. Cross-multiply to solve for [tex]\( S \)[/tex]:
[tex]\[
S \times 5 = 2 \times 30
\][/tex]
[tex]\[
5S = 60
\][/tex]
6. Solve for the smaller number:
[tex]\[
S = \frac{60}{5}
\][/tex]
[tex]\[
S = 12
\][/tex]
Thus, the smaller number is [tex]\( \boxed{12} \)[/tex].
