Sure, I'd be happy to help!
To find the smaller number when two numbers are in the ratio [tex]\(2:5\)[/tex] and the bigger number is 30, follow these steps:
1. Understand the ratio: The ratio [tex]\(2:5\)[/tex] means that for every 2 units of the smaller number, there are 5 units of the bigger number.
2. Define variables:
- Let the smaller number be [tex]\(2x\)[/tex].
- Let the bigger number be [tex]\(5x\)[/tex].
3. Given value:
- The value of the bigger number is given as 30. Hence, [tex]\(5x = 30\)[/tex].
4. Solve for [tex]\(x\)[/tex]:
To find the value of [tex]\(x\)[/tex], solve the equation:
[tex]\[
5x = 30
\][/tex]
Divide both sides by 5:
[tex]\[
x = \frac{30}{5}
\][/tex]
[tex]\[
x = 6
\][/tex]
5. Find the smaller number:
Since the smaller number is represented as [tex]\(2x\)[/tex]:
[tex]\[
2x = 2 \times 6 = 12
\][/tex]
Therefore, the smaller number is [tex]\(12\)[/tex].
